Question

The height of a right circular cylinder is 10.5 m. If three times the sum of the areas of ots two circular faces is twice the area of the curved surface area. Find the radius of its base.

Answer 1

Height of cylinder=10.5m
Let r be the radius and h be the height of a right circular cylinder, then
Area of its circular faces= $2\pi r^2$
and area of curved surface= $2\pi rh$
Now, according to the condition:
$3\times 2\pi r^2=2\times 2\pi rh$
$\Rightarrow 6\pi r^2=4\pi rh\Rightarrow 3r=2h$
$\Rightarrow r=\frac{2h}{3}$
$=\frac{2}{3}\times 10.5m=2\times 3.5=7m$