If the curved surface area of a cylindrical pillar is 264m² and it's volume is 924m³, then find the height and diameter

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 height and diameter.

Solution: 

Let the radius of the base of the cylinder be $r$ and the height be $h$.

The curved surface area of a cylinder of radius r and height $h = 2\pi rh$ 

Therefore,

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

$264(7) = 44rh$

$h=\frac{42}{r}\ m$.....(i)

Volume of the cylinder $=\pi r^2h$

$924=\frac{22}{7} \times r^2 \times \frac{42}{r}$         [From (i)]

$42=6r$

$r=\frac{42}{6}$

$r=7\ m$

This implies,

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

$h=6\ m$

Diameter$=2r=2(7)\ m=14\ m$.

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Updated on: 10-Oct-2022

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