Question

A cylindrical metal pipe, 1m long, has inner and outer radii of 3. 7cm and 2. 3cm respectively. Use the value 22/7 for pi to find the volume of metal in the pipe?

Answer 1

`2640 \:cm^3`

Explanation:

The given solid is a hollow cylinder and we are asked to calculate the volume of the solid part

The volume of the solid part is given by
V = π (R² - r²) h

where
R = outer radius

r = inner radius

h = height of the hollow cylinder

Since R² - r² = (R + r)(R - r) we can rewrite the volume equation as
V = π(R + r)(R - r)h (I am only doing this for easier computation manually)

We are given
R = 3.7cm, r = 2.3cm and h = 1m

Note that height is in meters so convert to cm
1 m = 100 cm
So h = 100 cm

Plugging in known values

`V = (22)/(7)(3.7 + 2.3)(3.7-2.3)100\\\\= \frac{22} {7}(6.0) (1.4) 100\\\\= 22 * 6 * 0.2 * 100 \quad\quad(1.4/7 = 0.2)\\\\= 2640 \:cm^3`