Question

The height and the radius of the base of a closed cylinder are in the ratio 3: 1. If its volume is 1029 $\pi c{m}^3;$ then its outer surface area is 526 $c{m}^2$

• A. True
• B. False

Answer 1

The correct option is B False

Given height and radius of cylinder are in ratio 3 : 1. volume of cylinder is 1029 $\pi {cm}^3$.
Let the radius of cylinder be$r$ then height of cylinder be $3r$.
Volume of cylinder $=\pi r^{2}h$
$1029\pi =\pi \times r^2\times 3r$
$\frac{1029\pi }{3\pi }=r^3,r^3=343r=\sqrt[3]{3343}=7cm$
Radius = 7 cm.
Height $=3r$=$3\times 7=$ 21 cm
Total surface area $=2\pi r(r+h)=2\times \frac{22}{7}\times 7\times (7+21)=2\times \frac{22}{7}\times 7\times 28=1232{cm}^2$