The curved surface area of a cylindrical pillar is $264\ m^2$ and its volume is $924\ m^3$. Find the diameter and the height of the pillar.

 Given:

The curved surface area of a cylindrical pillar is $264\ m^2$ and its volume is $924\ m^3$.

To do:

We have to find the diameter and the height of the pillar.

Solution:

Curved surface area of the pillar $= 264\ m^2$

Volume of the pillar $= 924\ m^3$

Let $r$ be the radius and $h$ be the height.

This implies,

$2\pi rh = 264$

$\frac{2 \times 22}{7} r h=264$

$r h=\frac{264 \times 7}{2 \times 22}$

$r h=42$.............(i)

$\pi r^{2} h=924$

$\frac{22}{7} r^{2} h=924$

$r^{2} h=\frac{924 \times 7}{22}$

$r^{2} h=294$..............(ii)

Dividing (ii) by (i), we get,

$r=\frac{294}{42}$

$r=7$

$r h=42$

$\Rightarrow 7 h=42$

$\Rightarrow h=\frac{42}{7}$

$\Rightarrow h=6$

Diameter $=2 r$

$=2 \times 7$

$=14 \mathrm{~m}$

Height $=6 \mathrm{~m}$

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Updated on: 10-Oct-2022

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