Question

The slant height of a frustum of a cone is 4 cm and perimeter of its circular end are 18 cm and 6 cm . Find the curved surface area and volume of the frustum

Answer 1

Given slant height(l)=4cm
Circumference1(C1)=18cm
2 pie r1 = 18cm
2*22/7*r1 = 18cm
therefore,
         r1 = 63/22cm
similarily
      C2 = 6cm
so,
    r2 = 21/22cm
now CSA of the frustum of cone = pie l (r1+r2)
= 22/7*4(63/22+21/22)
= 84/22 * 4 * 22/7
= 48 sq. cm.

Answer 2

Given,

Slant height of frustum of cone (l) = 4 cm

Let ratio of the top and bottom circles be r1 and r2

And given perimeters of its circular ends as 18 cm and 6 cm

⟹ 2πr1 = 18 cm; 2πr2 = 6 cm

⟹ πr1= 9 cm and πr2 = 3 cm

We know that,

Curved surface area of frustum of a cone = π(r1 + r2)l

= (πr1+πr2)l = (9 + 3) × 4

 = (12) × 4 = 48 cm2

Therefore, the curved surface area of the frustum = 48 cm2.