Question

The sum of the base radius and the height of a solid right circular solid cylinder is $37cm$.If the total surface area of the cylinder is $1628sq.cm$, then find the volume of the cylinder.

• A. $4620{cm}^2$
• B. $4220{cm}^2$
• C. $8620{cm}^2$
• D. None of these

Answer 1

The correct option is A $4620{cm}^2$

Given in cylinder

$r+h=37cm...\left(1\right)$

Total surface area $=2\pi r^2+2\pi rh=1628cm$

$\Rightarrow 2\pi (r^2+rh)=1628$

$\Rightarrow r(r+h)=259$

From (1) $\Rightarrow r\left(37\right)=259$

$r=7cm$

(1) $\Rightarrow h=30cm$

Volume $=\pi r^{2}h=\frac{22}{7}\times 7^2\times 30$

$=4620c{m}^2$