Question

A friction clutch in the form of the frustum of a cone, the diameters of the ends being 8cm, and 10 cm and length 8 cm. Find its bearing surface and its volume. [Take π = 3.14]

Answer 1

We have,

Diameter of one end = 10cm

So, radius (R) = 5cm

Diameter of other end = 8cm

So, radius (r) = 4cm

and slant height, l = 8cm

So, height, h = √{l² – (R – r)²}

= √{(8)² – (5 – 4)²

= √64 – (1)²

= √64 – 1

= √63

= 7.937 cm

Bearing surface of the clutch = CSA of the frustum

= πl (R + r)

= 3.14 × 8 (5 + 4)

= 25.12 (9)

= 226.08 cm²

= 506.75 cm³

Hence, Volume of frustum = 506.75 cm³