Question

The curved surface area of the frustum of a cone is $48c{m}^2$. If the perimeters of circular ends are 18 cm and 6 cm, then its slant height is

• A. 6 cm
• B. 4 cm
• C. 5 cm
• D. 8 cm

Answer 1

The correct option is B 4 cm

Let the upper radius and lower radius of frustum of cone be r and R respectively, and slant height be l.

CSA of frustum of cone $=48c{m}^2$

⇒ π(R + r)l = 48 ….. (i)

Perimeters of circular ends are 18 cm and 6 cm.

∴2πR = 18 cm and 2πr = 6 cm

⇒ πR = 9 cm and πr = 3 cm ….. (ii)

From (i) and (ii), (πR + πr)l = 48

⇒ (9 + 3) × l = 48

⇒ 12 × l = 48

⇒ l = 4 cm

Hence, the correct answer is option (b).