# The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum

**Solution:**

A figure is drawn to visualize the shape.

Using the circumferences of the circular ends of the frustum to find the radii of its circular ends.

Circumference of the circle = 2πr, where r is the radius of the circle

Let us find the CSA of the frustum by using the formula;

CSA of a frustum of a cone = π(r_{1} + r_{2})l, where r_{1}, r_{2,} and l are the radii and slant height of the frustum of the cone respectively.

Slant height of frustum of a cone, l = 4 cm

Circumference of the larger circular end, C_{1} = 18 cm

Radius of the larger circular end, r = C_{1} = 18 cm = 9 cm

Circumference of the smaller circular end, C_{2} = 6 cm

Radius of the smaller circular end, r_{2} = C_{2 }/ 2π = 6 cm / 2π = 3 cm

CSA of frustum of a cone = π (r_{1} + r_{2}) l

= π (9/π cm + 3/π cm) × 4 cm

= 48 cm^{2}

The curved surface area of the frustum is 48 cm^{2}.

**Video Solution:**

## The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum

### NCERT Solutions for Class 10 Maths - Chapter 13 Exercise 13.4 Question 2 :

The slant height of a frustum of a cone is 4 cm and the perimeters (circumference) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum

The curved surface area of the frustum of slant height 4 cm having circumference of its circular ends as 18 cm and 6 cm is 48 cm^{2}