Question

A solid cylinder has a total surface area of 231 cm². Its curved surface area is $\frac{2}{3}$ of the total surface area. Find the volume of the cylinder.

Answer 1

We know that the total surface area of the cylinder is 231 cm² and the curved surface area is 2/3 of the total surface area.
So, the curved surface area is:
2/3 $\times$ (231 cm²) = 154 cm²

Then, the radius of the cylinder can be calculated in the following manner:
Curved surface area = 2πrh
​154 cm² = 2πrh ... (1)
Here, r cm is the radius of the cylinder and h cm is the length of the cylinder.
2πr² = (231-154) cm² = 77 cm²
77 cm² = 2π​r²
From here, the radius (r) can be calculated in the following manner:

$r=\sqrt{\frac{77}{2\times {\displaystyle \frac{22}{7}}}}$
r = 3.5 cm

Substituting this result into equation (1):
154 cm² = 2π(3.5 cm)h
h= 154 cm² / (2x 22 x (3.5cm))
7
h = 7 cm

∴ V = π​r²h = $\frac{22}{7}$ ​x (3.5 cm)² x (7 cm) = 269.5 cm³

Hence, the volume of the cylinder is 269.5 cm³.