Question

A fraction 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.[Take $\pi =3.14$]

Answer 1

Diameter of ends are $32cm$ and $20cm$

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

$l=\sqrt{h^2+{(r_1-r_2)}^2}$

$=\sqrt{8^2+{(16-10)}^2}$

$=\sqrt{100}=10cm$

Total surface area $=\pi \left[\right(r_1+r_2)l+{r_1}^2+{r_2}^2]$

$=\pi \left[(16+10)10+{16}^2+{10}^2\right]$

$=616\pi {cm}^2$

and volume $=\frac{\pi }{3}[{r_1}^2+r_1{r}_2+{r_2}^2]h$

$=\pi [256{cm}^2+160{cm}^2+100{cm}^2]8cm$

$=1376\pi {cm}^3$