Question

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

Answer 1

Given: Curved Surface Area of cylinder = $264m^2$

Volume of cylinder = $924m^3$

CSA of cylinder = $2\pi rh$

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

$r\times h=42$

$h=\frac{42}{r}...\left(1\right)$

Volume of cylinder = $\pi r^{2}h$

$924=\frac{22}{7}\times r^2\times \frac{42}{r}$

$924=\frac{22}{7}\times r\times 42$

$r=\frac{924\times 7}{22\times 42}$

$r=7m.$

Radius is $7m$

diameter is $14m$

Height of cylinder = $\frac{42}{7}=6m$