Question

A friction clutch is in the form of a frustum of a cone, the diameter of the ends being $32cm$ and $20cm$ and length $8cm$. Find its bearing surface and volume.

Answer 1

Let ABB'A be the friction clutch of slant height $l$ cm

We have
$r_1=16cm,r_2=10cm$ and $h=8cm$

$l^2=h^2+{(r_1-r_2)}^2\Rightarrow l^2=64+36\Rightarrow l=10cm$

Now Bearing surface of the clutch $=$ lateral surface of the furstum

$=\pi (r_1+r_2)l$

$=\frac{22}{7}\times (16+10)\times 10{cm}^2$$

$=817.14{cm}^2$

Volume $=\frac{1}{3}\pi (r_1^2+r_2^2+r_1{r}_2)h$

$=\frac{1}{3}\times \frac{22}{7}\times 8\times ({16}^2+16\times 10+{10}^2){cm}^3$

$=\frac{176}{21}\times 516{cm}^3$

$=4324.57{cm}^3$