Question

The ratio between the curved surface area and the total surface area of a right circular cylinder is 1 : 2. Find the volume of the cylinder, if its total surface area is 616 cm².

Answer 1

Let r cm be the radius and h cm be the length of the cylinder. The curved surface area and the total surface area is 1:2.
The total surface area is 616 cm².
The curved surface area is the half of 616 cm², i.e. 308 cm²​.
Curved area = 2πrh
So,
\[h = \frac{308}{2\pi r}\]
Total surface area = Curved surface area + Top and bottom area
Top and bottom area = 616 - 308 = 308 cm² = 2πr²

\[r^2 = \frac{308}{2 \times \frac{22}{7}}\]

r = 7 cm

\[r^2 = \frac{308}{2 \times \frac{22}{7}}\]

Then, the volume of the cylinder can be calculated as follows:

\[V = \frac{22}{7} \times 7^2 \times 7 = 1078\]

Hence, it is obtained that the volume of the cylinder is 1078 cm³.