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The perimeter of the base of a cylinder is 10 cm. The height of the cylinder is 20 cm. Find its volume.
- a)500/π cm3
- b)500 π cm3
- c)200/π cm3
- d)200 π cm3
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
The perimeter of the base of a cylinder is 10 cm. The height of the cy...
Base of a cylinder is circular, Perimeter of a circle = 2πr
⇒ 2πr = 10
⇒ r = 5/π
Volume of the cylinder = πr2h = π × (5/π)2 × 20
= 500/π cm3
⇒ 2πr = 10
⇒ r = 5/π
Volume of the cylinder = πr2h = π × (5/π)2 × 20
= 500/π cm3
Most Upvoted Answer
The perimeter of the base of a cylinder is 10 cm. The height of the cy...
Understanding the Problem
To find the volume of the cylinder, we need the radius and height. We are given:
- Perimeter (circumference) of the base = 10 cm
- Height of the cylinder = 20 cm
Step 1: Find the Radius
The formula for the circumference (C) of a circle is given by:
C = 2 * π * r
Where:
- C is the circumference
- r is the radius
From the given perimeter:
10 = 2 * π * r
To find the radius (r):
r = 10 / (2 * π) = 5 / π cm
Step 2: Calculate the Volume
The formula for the volume (V) of a cylinder is:
V = π * r² * h
Where:
- r is the radius
- h is the height
Using the height given (20 cm):
V = π * (5 / π)² * 20
Calculating r²:
(5 / π)² = 25 / π²
Now plug this back into the volume formula:
V = π * (25 / π²) * 20
Step 3: Simplify the Volume Calculation
V = (25 * 20) / π = 500 / π cm³
Conclusion
The volume of the cylinder is:
- 500 / π cm³
Thus, the correct answer is option 'A': 500 / π cm³.
To find the volume of the cylinder, we need the radius and height. We are given:
- Perimeter (circumference) of the base = 10 cm
- Height of the cylinder = 20 cm
Step 1: Find the Radius
The formula for the circumference (C) of a circle is given by:
C = 2 * π * r
Where:
- C is the circumference
- r is the radius
From the given perimeter:
10 = 2 * π * r
To find the radius (r):
r = 10 / (2 * π) = 5 / π cm
Step 2: Calculate the Volume
The formula for the volume (V) of a cylinder is:
V = π * r² * h
Where:
- r is the radius
- h is the height
Using the height given (20 cm):
V = π * (5 / π)² * 20
Calculating r²:
(5 / π)² = 25 / π²
Now plug this back into the volume formula:
V = π * (25 / π²) * 20
Step 3: Simplify the Volume Calculation
V = (25 * 20) / π = 500 / π cm³
Conclusion
The volume of the cylinder is:
- 500 / π cm³
Thus, the correct answer is option 'A': 500 / π cm³.
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Community Answer
The perimeter of the base of a cylinder is 10 cm. The height of the cy...
Base of a cylinder is circular, Perimeter of a circle = 2πr
⇒ 2πr = 10
⇒ r = 5/π
Volume of the cylinder = πr2h = π × (5/π)2 × 20
= 500/π cm3
⇒ 2πr = 10
⇒ r = 5/π
Volume of the cylinder = πr2h = π × (5/π)2 × 20
= 500/π cm3
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The perimeter of the base of a cylinder is 10 cm. The height of the cylinder is 20 cm. Find its volume.a)500/π cm3b)500 π cm3c)200/π cm3d)200 π cm3Correct answer is option 'A'. Can you explain this answer?
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