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The height of a cylinder is 14 cm and its curved surface area is 264 sq. cm. Find the radius of its base.
- a)3 cm
- b)4 cm
- c)5 cm
- d)6 cm
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
The height of a cylinder is 14 cm and its curved surface area is 264 s...
Curved surface area of a cylinder = 2πrh
Given: h = 14 cm and curved surface area = 264 cm2
∴ 2πrh = 264
r = 3 cm
Given: h = 14 cm and curved surface area = 264 cm2
∴ 2πrh = 264
r = 3 cm
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Community Answer
The height of a cylinder is 14 cm and its curved surface area is 264 s...
Understanding the Problem
To find the radius of the base of a cylinder, we need to use the formula for the curved surface area (CSA) of a cylinder, which is given by:
Curved Surface Area (CSA) = 2 * π * r * h
Where:
- r = radius of the base
- h = height of the cylinder
Given Values
- Height (h) = 14 cm
- Curved Surface Area (CSA) = 264 sq. cm
Substituting Known Values
We can rearrange the formula to solve for the radius (r):
r = CSA / (2 * π * h)
Now, substituting the values we have:
r = 264 / (2 * π * 14)
Calculating Step-by-Step
1. Calculate the denominator:
- 2 * π * 14 ≈ 2 * 3.14 * 14 ≈ 87.92
2. Now substitute this back into the equation for r:
- r = 264 / 87.92 ≈ 3
Conclusion
Thus, the radius of the base of the cylinder is approximately 3 cm. Therefore, the correct answer is option 'A' (3 cm).
To find the radius of the base of a cylinder, we need to use the formula for the curved surface area (CSA) of a cylinder, which is given by:
Curved Surface Area (CSA) = 2 * π * r * h
Where:
- r = radius of the base
- h = height of the cylinder
Given Values
- Height (h) = 14 cm
- Curved Surface Area (CSA) = 264 sq. cm
Substituting Known Values
We can rearrange the formula to solve for the radius (r):
r = CSA / (2 * π * h)
Now, substituting the values we have:
r = 264 / (2 * π * 14)
Calculating Step-by-Step
1. Calculate the denominator:
- 2 * π * 14 ≈ 2 * 3.14 * 14 ≈ 87.92
2. Now substitute this back into the equation for r:
- r = 264 / 87.92 ≈ 3
Conclusion
Thus, the radius of the base of the cylinder is approximately 3 cm. Therefore, the correct answer is option 'A' (3 cm).
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The height of a cylinder is 14 cm and its curved surface area is 264 sq. cm. Find the radius of its base.a)3 cmb)4 cmc)5 cmd)6 cmCorrect answer is option 'A'. Can you explain this answer?
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