Question

The ratio between the radius of the base and the height of a cylinder is 2 : 3. Find the total surface area of the cylinder, if its volume is 1617 cm³.

Answer 1

Let r cm be the radius and h cm be the height of the cylinder. It is given that the ratio of r and h is 2:3, so h = 1.5r
The volume of the cylinder (V) is 1617 cm³.

So, we can find the radius and the height of the cylinder from the equation given below:
V= πr²h
1617 = πr²h
1617 = πr²(1.5r)
r³ =343
r = 7 cm and h = 10.5 cm

Total surface area = 2πr²+2πrh
​ =$2\times \frac{22}{7}\times 7^2+2\times \frac{22}{7}\times 7\times 10.5=770{\mathrm{cm}}^2$

Hence, the total surface area of the cylinder is 770 cm².