Question

The height of a circular cylinder is 4.2cm. There times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder correct to 1 decimal place.

Answer 1

Height of the cylinder (h) = 4.2cm
Let r be the radius of the cylinder
Sum of the area of 2 circular faces = πr² + πr²
Curved surface area of cylinder = 2π rh
Given that:
3 x (πr² + πr²) = 2 x 2π rh
6πr² = 4π rh
6r = 4h
6r = 4 x 4.2

r = `(16.8)/(6)`
r = 2.8cm
∴ Volume of the cylinder
= π x r² x h

= `(22)/(7) xx 2.8^2 xx 4.2`
= 103.5cm³.