Find the floor area of the steam room of the bathhouse under construction, give the answer in square meters
Find the volume of the steam room of the bathhouse under construction.
Give your answer in cubic meters. The owner of a summer cottage is building a bathhouse with a steam room. The steam compartment has dimensions: length 3.5 m, width 2.2 m, height 2 m. There are no windows in the steam compartment; for access inside, a door 60 cm wide is planned, the height of the doorway is 1.8 m. To warm up the steam compartment, you can use electric or wood stove. The table shows the characteristics of three furnaces.
| Furnace number | Type | Room volume | Weight | Price |
| 1 | Wood-burning | 8-12 | 40 | 18 000 |
| 2 | Wood-burning | 10-16 | 48 | 19 500 |
| 3 | Electric | 9-15,5 | 15 | 15 000 |
There are no additional costs required to install a wood stove. Installing an electric stove will require a special cable, which will cost 6,500 rubles.
Establish a correspondence between the volumes of the room and the numbers of the stoves for which this volume is the smallest for space heating. Fill out the table and transfer the sequence of three numbers into the answer form without spaces, commas or other additional characters.
| Volume | 8 | 9 | 10 |
| Furnace number |
The table shows that the smallest volume for the first furnace is 8, for the second - 10, and for the third - 9.
Source
Bathhouse problem. OGE grade 9. Productive task
WORKSHEET. Student__________________________
Bathhouse problem.
Read the text carefully and complete tasks 1-5.
The owner of a summer cottage is building a bathhouse with a steam room. Dimensions of the steam room: length 3.2 m, width 2.1 m, height 2.5 m. To heat the steam room, you can use an electric or wood stove. Three possible options are given in the table.
There are no additional costs required to install a wood stove. Installing an electric stove will require a special cable, which will cost 7,000 rubles. In addition, the owner calculated that in a year the electric furnace will consume 2800 kilowatt-hours of electricity at 3 rubles. for 1 kilowatt-hour, and a wood-burning stove will consume 3.5 cubic meters per year. m of firewood, which will cost 1600 rubles. for 1 cubic m.
A wood stove has a casing around the firebox door. The upper part of the casing is made in the form of an arch, welded to the front wall along a circular arc (see figure).
BEFORE READING
Training task 1.
Scanning reading skills, predicting text content.
Review the text, table, and image. What will the text tell you?
WHILE READING.
Training task 2.
Ability to find information.
Read the text. As you read, write down answers to questions using key words that will help you solve problems in the future. Match the text, table and image.
AFTER READING.
Training task 3.
The ability to establish a correspondence between the content and mathematical model of an object depending on the conditions of the problem.
Solve problems.
Use hints. Write down the solution and answer.
SOLUTION ANSWER
1. Find the volume of the steam room of the bathhouse under construction (in cubic meters).
The volume of which geometric body needs to be found?
Write down the formula to find the volume of this body?
Calculate the volume. What are the units of measurement?
Answer:
2. How many rubles will a wood-burning stove, suitable for the heated volume of a steam compartment, cost less than an electric one, taking into account installation?
Using the answer to problem 1, choose which wood-burning stove is suitable for the heated volume of the steam room? Use the table to determine its cost.
Calculate the cost of an electric furnace including installation.
What mathematical operation must be performed to find how much one number is greater or less than another?
Complete this action.
Answer:
3. How many rubles will the operation of a wood-burning stove, which is suitable for the heated volume of the steam compartment, cost less than the operation of an electric one for a year?
Using the text, calculate how many rubles it would cost to use a wood stove for a year?
Using the text, calculate how many rubles it will cost to use an electric oven for a year?
What mathematical operation must be performed to find how much one number is greater or less than another?
Complete this action.
Answer:
4. Delivery of the stove from the store to the site costs 700 rubles. When purchasing a stove with a price above 20,000 rubles, the store offers a 3% discount on the product and 30% on delivery. How much will it cost to purchase a Vulcan stove along with delivery under these conditions?
Using the table, check when purchasing a Vulcan stove whether the store will provide discounts?
How to find the percentage of a number?
Calculate the discounted price of the stove.
Calculate the discounted shipping cost.
Calculate the purchase price.
Answer:
5. The owner chose a wood stove. A drawing of the furnace is shown in Fig. 2. Dimensions are indicated in cm. To install the stove, the owner needed to know the arch radius R. The dimensions of the casing are shown in the figure. Find the radius in centimeters; Round your answer to tenths.
Study the geometric model of this problem.
OA=OD=OB=R
CD=
OC=
CB=
Determine the type of triangle OW? What theorem can you use to write the equation?
Write and solve the equation.
To what digit should you round? (Underline).
What number comes after the underlined one?
Perform rounding. Write down only the number you receive as your answer.
Answer:
Training task 4.
Ability to check the solution to a problem. The ability to analyze the used mathematical solution methods from the point of view of their rationality for studying a real object.
Determine whether the obtained result corresponds to the conditions of the problem. Determine whether the resulting number corresponds to its range of values.
Check the answers.
Training task 5.
The ability to plan your actions.
Create an algorithm for solving a practice-oriented problem of this type.
Find the floor area of the steam room of the bathhouse under construction, give the answer in square meters
Find the area of the ceiling of the steam room of the bathhouse under construction. Give your answer in square meters.
The owner of a summer cottage is building a bathhouse with a steam room. The steam compartment has dimensions: length 3.5 m, width 2.2 m, height 2 m. There are no windows in the steam compartment; for access inside, a door 60 cm wide is planned, the height of the doorway is 1.8 m. To warm up the steam compartment, you can use electric or wood stove. The table shows the characteristics of three furnaces.
| Furnace number | Type | Room volume | Weight | Price |
| 1 | Wood-burning | 8-12 | 40 | 18 000 |
| 2 | Wood-burning | 10-16 | 48 | 19 500 |
| 3 | Electric | 9-15,5 | 15 | 15 000 |
There are no additional costs required to install a wood stove. Installing an electric stove will require a special cable, which will cost 6,500 rubles.
Establish a correspondence between the volumes of the room and the numbers of the stoves for which this volume is the smallest for space heating. Fill out the table and transfer the sequence of three numbers into the answer form without spaces, commas or other additional characters.
| Volume | 8 | 9 | 10 |
| Furnace number |
The table shows that the smallest volume for the first furnace is 8, for the second - 10, and for the third - 9.
Source
Training version No. 7 and No. 8 print and solve the OGE 2022 in mathematics grade 9 with answers
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New training options No. 7 and No. 8 OGE 2022 in mathematics grade 9 with answers and solutions, print and solve on the website using the new FIPI demo version of the OGE exam 2022 to prepare for the exam.
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Print and solve OGE 2022 in mathematics option No. 7 and No. 8
Answers for options
Answers and tasks for option 7:
The owner of a summer cottage is building a bathhouse with a steam room. The steam compartment has dimensions: length 3.4 m, width 2 m, height 2.1 m. There are no windows in the steam compartment; for access inside, a door 62 cm wide is planned, the height of the doorway is 1.8 m.
To warm up the steam compartment, you can use an electric or wood stove. The table shows the characteristics of three furnaces. There are no additional costs required to install a wood stove. Installing an electric stove will require a special cable, which will cost 6,800 rubles.
1) Establish a correspondence between the masses and numbers of furnaces. Fill out the table and transfer the sequence of three numbers into the answer form without spaces, commas or other additional characters.
Answer: 321
2) Find the floor area of the steam room of the bathhouse under construction. Give your answer in square meters.
Answer: 6.8
3) How many rubles will it cost to purchase an electric stove with installation and delivery, if delivery of the stove to a summer cottage costs 1000 rubles?
Answer: 27300
4) Delivery of any stove from the store to the site costs 800 rubles. When purchasing a stove costing more than 20,000 rubles, the store gives a 15% discount on the product and 20% on delivery. How many rubles will it cost to purchase stove number 1 with delivery under these conditions?
Answer: 19340
5) The owner chose a wood-burning stove (Fig. 1). A drawing of the front panel of the stove is shown in Figure 2. The stove is equipped with a casing around the firebox door. The upper part of the casing is made in the form of an arch, welded to the front wall of the stove along an arc of a circle with the center in the middle of the lower part of the casing (see Fig. 2). To install the stove, the owner needed to know the radius of curvature of the arch R. The dimensions of the casing in centimeters are shown in the figure. Find the radius of the arch in centimeters.
Answer: 55
10) The taxi company currently has 20 cars available: 2 black, 13 yellow and 5 green. One of the cars, which happened to be closest to the customer, responded to the call. Find the probability that a yellow taxi will come to him.
Answer: 0.65
14) There are 13 rows in the amphitheater. There are 14 seats in the first row, and each next row has 2 more seats than the previous one. How many seats are there in the amphitheater?
Answer: 338
15) In triangle ABC it is known that AC = 25, BM is the median, BM = 23. Find AM.
Answer: 12.5
16) Quadrilateral ABCD is inscribed in a circle. Angle ABD is 38°, angle CAD is 33°. Find angle ABC. Give your answer in degrees.
Answer: 71
17) The area of a parallelogram is 120, and its two sides are 10 and 15. Find its heights. Please indicate greater height in your answer.
Answer: 12
18) Find the tangent of the angle AOB shown in the figure.
Answer: 0.2
19)Which of the following statements is true? 1) In a right triangle, the square of the hypotenuse is equal to the difference of the squares of the legs. 2) If the diagonals in a parallelogram are equal and perpendicular, then this parallelogram is a square. 3) The point of intersection of two circles is equidistant from the centers of these circles. In response, write down the number of the selected statement.
Answer: 2
21) Two cars simultaneously set off on an 840-kilometer journey. The first one drives at a speed 4 km/h higher than the second one and arrives at the finish line 1 hour earlier than the second one. Find the speed of the first car.
Answer: 60
23) Point H is the base of the altitude drawn from the vertex of right angle B of triangle ABC to the hypotenuse AC. Find AB if AH=8, AC-32.
Answer: 16
24)In the trapezoid PRST with bases RS and PT, the diagonals intersect at point M. Prove that the areas of triangles PRM and STM are equal.
25) In the parallelogram ABCD there is a diagonal AC. Point O is the center of a circle inscribed in triangle ABC. The distances from point O to point A and lines AD and AC are respectively 25, 14 and 7. Find the area of parallelogram ABCD.
Answer: 1008
Answers and tasks for option 8:
1) Establish a correspondence between the masses and numbers of furnaces. Fill out the table and transfer the sequence of three numbers into the answer form without spaces, commas or other additional characters.
Answer: 132
2) Find the area of the ceiling of the steam room of the bathhouse under construction. Give your answer in square meters.
Answer: 7
3) How many rubles will it cost to purchase an electric stove with installation and delivery, if delivery of the stove to a summer cottage costs 800 rubles?
Answer: 25200
4) Delivery of any stove from the store to the site costs 1000 rubles. When purchasing a stove costing more than 15,000 rubles, the store offers 5% discounts on goods and 25% on delivery. How many rubles will it cost to purchase stove number 1 with delivery under these conditions?
Answer: 16425
10) The taxi company currently has 20 cars available: 3 black, 11 yellow and 6 green. One of the cars, which happened to be closest to the customer, responded to the call. Find the probability that a yellow taxi will come to him.
Answer: 0.55
14) There are 14 rows in the amphitheater. There are 13 seats in the first row, and each next row has 2 more seats than the previous one. How many seats are there in the amphitheater?
Answer: 364
15) In triangle ABC it is known that AC = 15, BM is the median, BM = 27. Find AM.
Answer: 7.5
16) Quadrilateral ABCD is inscribed in a circle. Angle ABD is 63°, angle CAD is 35°. Find angle ABC. Give your answer in degrees.
Answer: 98
17) The area of the parallelogram is 144, and its two sides are 18 and 12. Find its heights. Please indicate greater height in your answer.
Answer: 12
19)Which of the following statements is true? 1) The length of the hypotenuse of a right triangle is less than the sum of the lengths of its legs. 2) If the diagonals of a convex quadrilateral are equal and perpendicular, then this quadrilateral is a square. 3) An angle inscribed in a circle is equal to the corresponding central angle based on the same arc. In response, write down the number of the selected statement.
Answer: 1
21) Two cars simultaneously set off on a 990-kilometer journey. The first one drives at a speed 9 km/h higher than the second one and arrives at the finish line 1 hour earlier than the second one. Find the speed of the first car.
Answer: 99
24) In the trapezoid DEFG with bases EF and DG, the diagonals intersect at point K. Prove that the areas of triangles DEK and FGK are equal.
25) In the parallelogram ABCD there is a diagonal AC. Point O is the center of a circle inscribed in triangle ABC. The distances from point O to point A and lines AD and AC are respectively 25, 15 and 7. Find the area of parallelogram ABCD.
Answer: 924
Other training options for the OGE 2022 in mathematics, grade 9:
10/05/2021 mathematics 9th grade options MA2190101-MA2190104 OGE 2022 statgrad with answers
Mathematics 9th grade work statgrad OGE 2022 options MA2190201-MA2190204
Find the floor area of the steam room of the bathhouse under construction, give the answer in square meters
Find the total area of the walls of the steam room of the bathhouse under construction (excluding the area of the door). Give your answer in square meters.
The owner of a summer cottage is building a bathhouse with a steam room. The steam compartment has dimensions: length 3.5 m, width 2.2 m, height 2 m. There are no windows in the steam compartment; for access inside, a door 60 cm wide is planned, the height of the doorway is 1.8 m. To warm up the steam compartment, you can use electric or wood stove. The table shows the characteristics of three furnaces.
| Furnace number | Type | Room volume | Weight | Price |
| 1 | Wood-burning | 8-12 | 40 | 18 000 |
| 2 | Wood-burning | 10-16 | 48 | 19 500 |
| 3 | Electric | 9-15,5 | 15 | 15 000 |
There are no additional costs required to install a wood stove. Installing an electric stove will require a special cable, which will cost 6,500 rubles.
Establish a correspondence between the volumes of the room and the numbers of the stoves for which this volume is the smallest for space heating. Fill out the table and transfer the sequence of three numbers into the answer form without spaces, commas or other additional characters.
| Volume | 8 | 9 | 10 |
| Furnace number |
The table shows that the smallest volume for the first furnace is 8, for the second - 10, and for the third - 9.
Source
Find the floor area of the steam room of the bathhouse under construction, give the answer in square meters
Find the area of the ceiling of the steam room of the bathhouse under construction. Give your answer in square meters.
The owner of a summer cottage is building a bathhouse with a steam room. The steam compartment has dimensions: length 3.5 m, width 2.2 m, height 2 m. There are no windows in the steam compartment; for access inside, a door 60 cm wide is planned, the height of the doorway is 1.8 m. To warm up the steam compartment, you can use electric or wood stove. The table shows the characteristics of three furnaces.
| Furnace number | Type | Room volume | Weight | Price |
| 1 | Wood-burning | 8-12 | 40 | 18 000 |
| 2 | Wood-burning | 10-16 | 48 | 19 500 |
| 3 | Electric | 9-15,5 | 15 | 15 000 |
There are no additional costs required to install a wood stove. Installing an electric stove will require a special cable, which will cost 6,500 rubles.
Establish a correspondence between the volumes of the room and the numbers of the stoves for which this volume is the smallest for space heating. Fill out the table and transfer the sequence of three numbers into the answer form without spaces, commas or other additional characters.
| Volume | 8 | 9 | 10 |
| Furnace number |
The table shows that the smallest volume for the first furnace is 8, for the second - 10, and for the third - 9.
Source
