Question

The volume and the curved surface area of a cylinder are 1650 cm³ and 660 cm²respectively. Find the radius and height of the cylinder.

Answer 1

Curved surface area of the cylinder = 2πrh  =660 cm²     ... (1)
Volume of the cylinder = πr²h   =1650 cm³                     ... (2)

From (1) and (2), we can calculate the radius (r) and the height of cylinder (h).
We know the volume of the cylinder, i.e. 1650 cm³
∴  1650 = πr²h

\[h = \frac{1650}{\pi r^2}\]
Substituting h into (1):
660 = 2πrh

\[h = \frac{1650}{\pi r^2}\]
660r = 2(1650)
r = 5 cm
\[h = \frac{1650}{\pi r^2}\]
\[ = \frac{1650}{\frac{22}{7} \times 5^2} = 21 cm .\]

Hence, the radius and the height of the cylinder are 5 cm and 21 cm, respectively.