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If the curved surface area of a cylinder is 1320 cm2 and its base radius is 21 cm, then what is its total surface area?
- a)4092 cm2
- b)2084 cm2
- c)5104 cm2
- d)None of thesse
Correct answer is option 'A'. Can you explain this answer?
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If the curved surface area of a cylinder is 1320 cm2and its base radiu...
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If the curved surface area of a cylinder is 1320 cm2and its base radiu...
To find the total surface area of a cylinder, we need to consider both the curved surface area and the area of the two bases.
Given:
Curved surface area = 1320 cm²
Base radius = 21 cm
1. Curved Surface Area of a Cylinder:
The curved surface area of a cylinder can be calculated using the formula:
CSA = 2πrh
where CSA is the curved surface area, π is a constant (approximately 3.14), r is the radius, and h is the height of the cylinder.
In this case, the curved surface area is given as 1320 cm² and the radius is 21 cm. Let's assume the height of the cylinder is h.
1320 = 2π(21)h
Dividing both sides by 2π:
660 = 21h
h = 660/21
h ≈ 31.43 cm
So, the height of the cylinder is approximately 31.43 cm.
2. Base Area of a Cylinder:
The base area of a cylinder can be calculated using the formula:
Base Area = πr²
where r is the radius of the base.
In this case, the radius of the base is 21 cm.
Base Area = π(21)²
Base Area = π(441)
Base Area ≈ 1381.47 cm²
3. Total Surface Area:
The total surface area of a cylinder is the sum of the curved surface area and the areas of the two bases.
Total Surface Area = Curved Surface Area + 2(Base Area)
Total Surface Area = 1320 + 2(1381.47)
Total Surface Area = 1320 + 2762.94
Total Surface Area ≈ 4082.94 cm²
Therefore, the correct answer is option 'A' - 4092 cm².
Given:
Curved surface area = 1320 cm²
Base radius = 21 cm
1. Curved Surface Area of a Cylinder:
The curved surface area of a cylinder can be calculated using the formula:
CSA = 2πrh
where CSA is the curved surface area, π is a constant (approximately 3.14), r is the radius, and h is the height of the cylinder.
In this case, the curved surface area is given as 1320 cm² and the radius is 21 cm. Let's assume the height of the cylinder is h.
1320 = 2π(21)h
Dividing both sides by 2π:
660 = 21h
h = 660/21
h ≈ 31.43 cm
So, the height of the cylinder is approximately 31.43 cm.
2. Base Area of a Cylinder:
The base area of a cylinder can be calculated using the formula:
Base Area = πr²
where r is the radius of the base.
In this case, the radius of the base is 21 cm.
Base Area = π(21)²
Base Area = π(441)
Base Area ≈ 1381.47 cm²
3. Total Surface Area:
The total surface area of a cylinder is the sum of the curved surface area and the areas of the two bases.
Total Surface Area = Curved Surface Area + 2(Base Area)
Total Surface Area = 1320 + 2(1381.47)
Total Surface Area = 1320 + 2762.94
Total Surface Area ≈ 4082.94 cm²
Therefore, the correct answer is option 'A' - 4092 cm².
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