Question

The volume of a cylinder is 504$\mathrm{\pi }$ cm³ and height is 14 cm. Find its curved surface area and total surface area. Express answer in terms of $\mathrm{\pi }$.

Answer 1

Given:
Volume of the cylinder = 504$\mathrm{\pi }$ cm³
Height (h) = 14 cm
We need to find the radius of the cylinder to find the curved surface area and total surface area of the cylinder.
We know:
Volume of a cylinder = $\mathrm{\pi }$r²h
$\Rightarrow$504$\mathrm{\pi }$ = $\mathrm{\pi }$ × r² × 14
$\Rightarrow$r² = 36
$\Rightarrow$r = $\sqrt{36}$ cm = 6 cm
Thus, we have:
Curved surface area of the cylinder = 2$\mathrm{\pi }$rh
= 2$\mathrm{\pi }$ × 6 × 14
= 168$\mathrm{\pi }$ cm²
And,
Total surface area of the cylinder = 2$\mathrm{\pi }$r (r + h)
= 2$\mathrm{\pi }$ × 6 × (6 + 14)
= 240$\mathrm{\pi }$ cm²