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# The curved surface area of a cylindrical pillar is 264 m^{2} and its volume is 924 m^{3}. 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 m^{2}

⇒ 2 π r h = 264

⇒ π r h = 132 ------------> (i)

The volume of the cylindrical pillar is 924 m^{3}

⇒ π r^{2 }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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