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A day full of math games & activities. Find one near you.
The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and height of the pillar.
Let us find the parameters of the cylindrical pillar.
Answer: The diameter of the pillar is 14 m and the height of the pillar is 6 m.
Let us use the formula of curved surface area (CSA) and the volume of a cylinder and find the required diameter and height of the pillar.
Explanation:
Let the radius of the pillar be 'r' and the height of the pillar be 'h'.
Given that the CSA of the cylinder is 264 m2
⇒ 2 π r h = 264
⇒ π r h = 132 ------------> (i)
The volume of the cylindrical pillar is 924 m3
⇒ π r2 h = 924 -------------> (ii)
From equation (i) and (ii):
[π r h] × r = 924
⇒ [132] × r = 924
⇒ r = 924/132
⇒ r = 7 m
Substitute the value of r in equation (i)
⇒ π × 7 × h = 132
⇒ (22/7) × 7 × h = 132
⇒ h = 132 × (7/22) × 1/7
⇒ h = 132/ 22 = 6
⇒ h = 6 m
Now, diameter = 2r = 2 × 7 = 14 m
Therefore, the diameter of the pillar is 14 m, and the height of the pillar is 7 m.
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