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If the lateral surface area of a cylinder is 132 cm2 and its height is 7 cm, then its base diameter is
- a)5 cm.
- b)3 cm.
- c)6 cm.
- d)4 cm.
Correct answer is option 'C'. Can you explain this answer?
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If the lateral surface area of a cylinder is 132cm2 and its height is ...
To solve this problem, we need to use the formula for the lateral surface area of a cylinder. The formula is given as:
Lateral Surface Area = 2πrh
where Lateral Surface Area is the total surface area of the curved part of the cylinder, π is a mathematical constant approximately equal to 3.14, r is the radius of the base of the cylinder, and h is the height of the cylinder.
In this case, we are given that the lateral surface area is 132 cm² and the height is 7 cm. Let's substitute these values into the formula and solve for the radius.
132 = 2πr(7)
Dividing both sides of the equation by 2π(7), we get:
132 / (2π(7)) = r
To calculate this value, we can use a calculator. The approximate value for π is 3.14, so the equation becomes:
132 / (2(3.14)(7)) = r
Simplifying further,
132 / (6.28)(7) = r
132 / 43.96 = r
To get the radius, we divide 132 by 43.96:
r ≈ 3 cm
Now that we have the radius, we can find the base diameter by doubling the radius. Therefore, the base diameter is:
Diameter = 2r = 2(3) = 6 cm
Hence, the correct answer is option C: 6 cm.
Lateral Surface Area = 2πrh
where Lateral Surface Area is the total surface area of the curved part of the cylinder, π is a mathematical constant approximately equal to 3.14, r is the radius of the base of the cylinder, and h is the height of the cylinder.
In this case, we are given that the lateral surface area is 132 cm² and the height is 7 cm. Let's substitute these values into the formula and solve for the radius.
132 = 2πr(7)
Dividing both sides of the equation by 2π(7), we get:
132 / (2π(7)) = r
To calculate this value, we can use a calculator. The approximate value for π is 3.14, so the equation becomes:
132 / (2(3.14)(7)) = r
Simplifying further,
132 / (6.28)(7) = r
132 / 43.96 = r
To get the radius, we divide 132 by 43.96:
r ≈ 3 cm
Now that we have the radius, we can find the base diameter by doubling the radius. Therefore, the base diameter is:
Diameter = 2r = 2(3) = 6 cm
Hence, the correct answer is option C: 6 cm.
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If the lateral surface area of a cylinder is 132cm2 and its height is 7 cm, then its base diameter isa)5 cm.b)3 cm.c)6 cm.d)4 cm.Correct answer is option 'C'. Can you explain this answer?
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