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A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?
- a)Rs. 10,474
- b)Rs. 10,475
- c)Rs. 10,472
- d)Rs. 10,477
- e)Rs. 10,470
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A toy is made by mounting a hemisphere of radius 7 cm over a right cir...
Note that we need to paint only curved surface areas of hemisphere and cylinder.
Curved Surface Area of the hemisphere = 2πr2
Curved Surface Area of the hemisphere = 2πr2
Curved Surface Area of the right circular cylinder = 2πrh
Total surface area that is to be painted = (308 + 440) cm2 = 748 cm2
Cost of painting the toy = 748 x 14 = Rs. 10,472
Hence, option 3.
Most Upvoted Answer
A toy is made by mounting a hemisphere of radius 7 cm over a right cir...
Given: Radius of hemisphere = 7 cm, Radius of cylinder = 7 cm, Height of cylinder = 10 cm, Cost of painting = Rs. 14 per cm^2.
To find: Cost of painting the entire toy except the base.
Approach:
- Calculate the surface area of the hemisphere and the cylinder.
- Add the surface areas of the hemisphere and the cylinder to get the total surface area of the toy.
- Subtract the area of the base from the total surface area to get the area that needs to be painted.
- Multiply the area to be painted by the cost of painting per cm^2 to get the total cost of painting.
Calculation:
Surface area of the hemisphere = 2πr^2 = 2π(7)^2 = 98π cm^2
Surface area of the cylinder = 2πrh + 2πr^2 = 2π(7)(10) + 2π(7)^2 = 294π cm^2
Total surface area of the toy = Surface area of hemisphere + Surface area of cylinder = 98π + 294π = 392π cm^2
Area of the base = πr^2 = π(7)^2 = 49π cm^2
Area to be painted = Total surface area - Area of base = 392π - 49π = 343π cm^2
Cost of painting the entire toy except the base = Area to be painted × Cost of painting per cm^2 = 343π × 14 = Rs. 4778π ≈ Rs. 10,472 (rounded off to the nearest rupee).
Therefore, the correct answer is option 'C'.
To find: Cost of painting the entire toy except the base.
Approach:
- Calculate the surface area of the hemisphere and the cylinder.
- Add the surface areas of the hemisphere and the cylinder to get the total surface area of the toy.
- Subtract the area of the base from the total surface area to get the area that needs to be painted.
- Multiply the area to be painted by the cost of painting per cm^2 to get the total cost of painting.
Calculation:
Surface area of the hemisphere = 2πr^2 = 2π(7)^2 = 98π cm^2
Surface area of the cylinder = 2πrh + 2πr^2 = 2π(7)(10) + 2π(7)^2 = 294π cm^2
Total surface area of the toy = Surface area of hemisphere + Surface area of cylinder = 98π + 294π = 392π cm^2
Area of the base = πr^2 = π(7)^2 = 49π cm^2
Area to be painted = Total surface area - Area of base = 392π - 49π = 343π cm^2
Cost of painting the entire toy except the base = Area to be painted × Cost of painting per cm^2 = 343π × 14 = Rs. 4778π ≈ Rs. 10,472 (rounded off to the nearest rupee).
Therefore, the correct answer is option 'C'.
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A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?a)Rs. 10,474b)Rs. 10,475c)Rs. 10,472d)Rs. 10,477e)Rs. 10,470Correct answer is option 'C'. Can you explain this answer?
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A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?a)Rs. 10,474b)Rs. 10,475c)Rs. 10,472d)Rs. 10,477e)Rs. 10,470Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?a)Rs. 10,474b)Rs. 10,475c)Rs. 10,472d)Rs. 10,477e)Rs. 10,470Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?a)Rs. 10,474b)Rs. 10,475c)Rs. 10,472d)Rs. 10,477e)Rs. 10,470Correct answer is option 'C'. Can you explain this answer?.
A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?a)Rs. 10,474b)Rs. 10,475c)Rs. 10,472d)Rs. 10,477e)Rs. 10,470Correct answer is option 'C'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?a)Rs. 10,474b)Rs. 10,475c)Rs. 10,472d)Rs. 10,477e)Rs. 10,470Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A toy is made by mounting a hemisphere of radius 7 cm over a right circular cylinder of the same radius. (Flat surface of hemisphere coincides with that of the right circular cylinder.) Height of the clinder is 10 cm. What will be the cost of painting the entire toy except the base, if the cost of painting is Rs. 14 per cm2?a)Rs. 10,474b)Rs. 10,475c)Rs. 10,472d)Rs. 10,477e)Rs. 10,470Correct answer is option 'C'. Can you explain this answer?.
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