A friction clutch is in the form of a frustum of a cone, the diameter of the ends being 32cm - Maths - Surface Areas and Volumes

Question

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

Aakash Sharma · Accepted Answer

Given: Diameters of ends are 32 cm and 20 cm $\Rightarrow r_{1} = \frac{32}{2} cm = 16 cm and r_{2} = \frac{20}{2} cm=10 cm$ and h = 8 cm $\Rightarrow l = \sqrt{h^{2} + (r_{1} - r_{2})^{2}} = \sqrt{{(8 cm)}^{2} + (16 cm - 10 cm)^{2}} = \sqrt{64 {cm}^{2} + 36 {cm}^{2}} = \sqrt{100 {cm}^{2}} = 10 cm$ $Thus total surface area = π {(r_{1} + r_{2}) l + {r_{1}}^{2} + {r_{2}}^{2}} = π {(16 cm+10 cm) 10 cm+ (16 cm)^{2} + (10 cm)^{2}} = π {260 {cm}^{2} + 256 {cm}^{2} + 100 {cm}^{2}} = 616 π {cm}^{2}$ $and Volume = \frac{π}{3} {{r_{1}}^{2} + r_{1} r_{2} + {r_{2}}^{2}} h = \frac{π}{3} {256 {cm}^{2} + 160 {cm}^{2} + 100 {cm}^{2}} 8 cm = \frac{π}{3} \times 516 \times 8 {cm}^{3} = π 172 \times 8 {cm}^{3} = 1376 π {cm}^{3}$

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