Question

Question 114

Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, find its curved surface area.

Answer 1

Let the radius and height of the cylinder be r and h respectively.
Curved surface area of cylinder $=2\pi rh$
Area of bases $=\pi r^2$
Sum of areas of bases $=2\pi r^2$
According to the question,
$4\times Curvedsurfacearea=6\times Sumofareasofbases$
$=4\times 2\pi rh=6\times 2\pi r^2\Rightarrow 8\pi rh=12\pi r^2\Rightarrow 2h=3r\Rightarrow r=\frac{2}{3}h$
$\therefore r=\frac{2}{3}\times 12=8cm$ [$\because$ h = 12 cm, given]
$\therefore$ Curved surface area of the cylinder $=2\pi rh$
$=2\times \frac{22}{7}\times 8\times 12=\frac{44\times 8\times 12}{7}=603.428c{m}^2$