Chapter 12.3, Problem 2CK

To determine

To find: Theapproximate volume for paint of each thickness $0\cdot 1,0\cdot 01,0\cdot 001$ .

Answer to Problem 2CK

The approximate volumes for paint of each thickness $0\cdot 1,0\cdot 01,0\cdot 001$ are $24\pi ,2\cdot 4\pi ,0\cdot 24\pi$ respectively.

Explanation of Solution

Given information:

The radius of and height of the cylinder is.

  $r=10,h=12$

Calculation:

The approximate volume of cylinder is given by.

  $\begin{array}{c}V=\text{lateral}\text{area}\text{of}\text{cylinder}\times \text{thickness}\text{of}\text{paint}\\ V\approx \text{2}\pi rh\times t\end{array}$

Here, $r$ is the radius, $h$ is the height and $t$ is thickness.

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

  $\begin{array}{c}{V}_1\approx \text{2}\pi rh\times t\\ \approx \text{2}\pi \times 10\times 12\times 0\cdot 1\\ \approx 24\pi \end{array}$

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

  $\begin{array}{c}{V}_2\approx \text{2}\pi rh\times t\\ \approx \text{2}\pi \times 10\times 12\times 0\cdot 01\\ \approx 2\cdot 4\pi \end{array}$

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

  $\begin{array}{c}{V}_3\approx \text{2}\pi rh\times t\\ \approx \text{2}\pi \times 10\times 12\times 0\cdot 001\\ \approx 0\cdot 24\pi \end{array}$

Therefore, the approximate volumes for paint of each thickness $0\cdot 1,0\cdot 01,0\cdot 001$ are $24\pi ,2\cdot 4\pi ,0\cdot 24\pi$ respectively.