Question

A friction clutch is in the form of a frustum of a cone the diameter of the ends being 32cm and 20cm and height 8cm. Find iths curved surface area and volume?

Answer 1

Answer:

Curved surface area of frustum = 816.4m².

Volume of frustum of cone is  4320.64 cm³.

Step-by-step explanation:

Consider a frustum of a cone having top radius is 10 cm , bottom radius is 16 cm and height is 8 cm.

We have to find the curved surface area and volume of this frustum.

For a frustum , with radius of bottom (R) and radius of top (r) and height h  anf l is the lateral height $l=\sqrt{(R-r)^2+h^2}$, thus

Curved surface area of frustum = $\pi \times (R+r) \times l=\pi \times (R+r) \times \sqrt{(R-r)^2+h^2}$

and Volume of frustum = $\frac{1}{3} \times \pi \times h \times (r^2+rR+R^2)$

First calculate Curved surface area, Put known values,

Curved surface area of frustum = $\pi \times (R+r) \times l=\pi \times (R+r) \times \sqrt{(R-r)^2+h^2}$

Curved surface area of frustum = $\pi \times (10+16) \times \sqrt{(16-10)^2+8^2}$

Curved surface area of frustum = $\pi \times 26 \times \sqrt{(6)^2+8^2}$

Curved surface area of frustum = $\pi \times 26 \times \sqrt{36+64}$

Curved surface area of frustum = $\pi \times 26 \times10$

Curved surface area of frustum = 816.4m².

Now we calculate volume, by putting values,

volume of frustum = $\frac{1}{3} \times \pi \times h \times (r^2+rR+R^2)$

volume of frustum = $\frac{1}{3} \times \pi \times 8 \times (10^2+10 \times 16+16^2)$

volume of frustum = $\frac{1}{3} \times \pi \times 8 \times 516$

volume of frustum = $\frac{1}{3} \times 12961.92$

volume of frustum = $4320.64$

Thus, Volume of frustum of cone is  4320.64 cm³.

Answer 2

Answer:

CSA of Frustum = π ( R*2 + r r*2 )+ π ( R + r ) l

Volume = 1/3 π( R*2 +r*2 +R×r ) h

Use this equation for solving it