Chapter 12.3, Problem 3CK

To determine

To find: The exact volume of cylinder for thickness $0\cdot 1,0\cdot 01,0\cdot 001$ .

Answer to Problem 3CK

The exact volume of cylinder for thickness $0\cdot 1,0\cdot 01,0\cdot 001$ are $24\cdot 12\pi ,2\cdot 4\pi ,$ and $0\cdot 24\pi$ respectively.

Explanation of Solution

Given information:

The radius of and height of the cylinder is.

  $r=10,h=12$

Calculation:

The exact volume of cylinder can be calculated by subtracting the volume of inner cylinder from outer cylinder.

The volume of cylinder is given by.

  $\pi r^{2}h$

Here, $r$ is the radius, $h$ is the height.

Calculate the volume.

  $\begin{array}{c}\pi r^{2}h=\pi \times {10}^2\times 12\\ =1200\pi \end{array}$

Calculate the volume of cylinder for thickness $0\cdot 1$ .

  $\begin{array}{c}{V}_1=\pi \times {\left(10\cdot 1\right)}^2\times 12\\ =1224\cdot 12\pi \end{array}$

The exact volume of cylinder is.

  $\begin{array}{c}{V}_2=1224\cdot 12\pi -1200\pi \\ =24\cdot 12\pi \end{array}$

Calculate the volume of cylinder for thickness $0\cdot 01$ .

  $\begin{array}{c}{V}_3=\pi \times {\left(10\cdot 01\right)}^2\times 12\\ =1202\cdot 40\pi \end{array}$

The exact volume of cylinder is.

  $\begin{array}{c}{V}_4=1202\cdot 40\pi -1200\pi \\ =2\cdot 40\pi \end{array}$

Calculate the volume of cylinder for thickness $0\cdot 001$ .

  $\begin{array}{c}{V}_5=\pi \times {\left(10\cdot 001\right)}^2\times 12\\ =1200\cdot 24\pi \end{array}$

The exact volume of cylinder is.

  $\begin{array}{c}{V}_6=1200\cdot 24\pi -1200\pi \\ =0\cdot 24\pi \end{array}$

Therefore, the exact volume of cylinder for thickness $0\cdot 1,0\cdot 01,0\cdot 001$ are $24\cdot 12\pi ,2\cdot 4\pi ,$ and $0\cdot 24\pi$ respectively.