Question

The perimeters of the ends of the frustum of a cone are 96 cm and 68 cm. If the height of the frustum be 20 cm, find its radii, slant height, volume and total surface.

Answer 1

Let radii of the circular ends of the frustum are R and r respectively.

Given that Perimeter of one end = 96cm

⇒ 2πR = 96

⇒ r = 10.82 cm

It is given that height of the frustum = 20cm

So, Slant height, l = √{h² + (R – r)²}

= √{(20)² +(15.27 – 10.82)²

= √400 + (4.45)²

= √400 + 19.80

= √419.80

= 20.49 cm

Now,

= 10800.25 cm³

Total Surface Area of the frustum = πR² + πr² + πl(R+r)

= π[(15.27)² + (10.82)²+ 20.49×(15.27+10.82)]

= π[233.1729 + 117.0724 + 534.5841]

= 22/7 x 884.83

= 2780.89 cm²