Chapter 12, Problem 1E

To determine

The correct option of remaining volume of the cylinder on removing $10mm$ diameter cylinder is to be selected from the following four options:

  $26,712.8m{m}^3$

  $37,573.4m{m}^3$

  $43,661.2m{m}^3$

  $48,985.3m{m}^3$

Answer to Problem 1E

The correct option is B. The remaining volume of the cylinder is $V=37,573.4m{m}^3$

Explanation of Solution

Given:

  

  $\begin{array}{l}{d}_1=36mm\\ d_2=10mm\\ h=40mm\end{array}$

Concept Used:

The volume of cylinder is given by the following expression:

  $V=\pi r^{2}h$

Where,

Radius: $r$

Height of cylinder: $h$

Calculation:

The volume of cylinder of $36mm$ diameter is calculated as:

  $\begin{array}{l}{V}_1=\pi r_1{}^{2}h\\ V_1=\pi {\left(\frac{d_1}{2}\right)}^{2}h\\ V_1=\pi {\left(\frac{36}{2}\right)}^2\left(40\right)\\ V_1=40715.04m{m}^3\end{array}$

The volume of cylinder of $10mm$ diameter is calculated as:

  $\begin{array}{l}{V}_2=\pi r_2{}^{2}h\\ V_2=\pi {\left(\frac{d_2}{2}\right)}^{2}h\\ V_2=\pi {\left(\frac{10}{2}\right)}^2\left(40\right)\\ V_2=3141.59m{m}^3\end{array}$

Now, the volume of the figure when the $10mm$ diameter cylinder is removed is calculated as:

  $\begin{array}{l}V=V_1-V_2\\ V=40715.04m{m}^3-3141.59m{m}^3\\ V=37,573.4m{m}^3\end{array}$

Conclusion:

Hence, the volume of the figure when the $10mm$ diameter cylinder is removed is calculated as $V=37,573.4m{m}^3$ .