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.
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(r₁ + r₂)l, where r₁, r₂, 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, C₁ = 18 cm
Radius of the larger circular end, r = C₁/ 2π = 18 cm// 2π = 9/π cm
Circumference of the smaller circular end, C₂ = 6 cm
Radius of the smaller circular end, r₂ = C₂ / 2π = 6 cm / 2π = 3/π cm
CSA of frustum of a cone = π (r₁ + r₂) l
= π (9/π cm + 3/π cm) × 4 cm
= 48 cm2
The curved surface area of the frustum is 48 cm2.
☛ Check: NCERT Solutions for Class 10 Maths Chapter 13
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
Summary:
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. The curved surface area of the frustum is 48 cm2.
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