Chapter 12.3, Problem 5CYU

To determine

To find: the volume of the peg.

Answer to Problem 5CYU

The volume of the figure is $28.26{\text{cm}}^3$ .

Explanation of Solution

Given:

  

Calculation:

The volume V of the cylinder is given by the formula

  $V=B\cdot h$

where $B=\pi r^2$ is the area of the circle and h is the height the cylinder.

First find the volume of the cylinder whose diameter is 4 cm.

Since radius is half the diameter of a circle, so radius of the circle is $\frac{4}{2}$ cm that is 2 cm.

The area $B_1$ of the circle is given

  $\begin{array}{c}{B}_1=\pi r^2\\ =\pi {\left(2\right)}^2\\ =8\pi \\ \approx 8\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =25.12\end{array}$

Put $B=25.12$ and $h=1$ in the volume formula to find the volume.

Thus, the volume $V$ is

  $\begin{array}{c}{V}_1=B_1\cdot h\\ =\left(25.12\right)1\\ =25.12\end{array}$

Next, find the volume of the cylinder whose diameter is 2 cm.

Since radius is half the diameter of a circle, so radius of the circle is $\frac{2}{2}$ cm that is 1 cm.

The area $B_2$ of the circle is given

  $\begin{array}{c}{B}_2=\pi r^2\\ =\pi {\left(1\right)}^2\\ =1\pi \\ \approx 1\left(3.14\right)\left[Since\pi \approx 3.14\right]\\ =3.14\end{array}$

Put $B_2=3.14$ and $h=3$ in the volume formula to find the volume.

Thus, the volume $V_2$ is

  $\begin{array}{c}{V}_2=B_2\cdot h\\ =\left(3.14\right)3\\ =9.42\end{array}$

Therefore, the required volume V is

  $\begin{array}{c}V=V_1+V_2\\ =25.12+3.14\\ =28.26\end{array}$

Therefore, the volume of the figure is approximately $28.26{\text{cm}}^3$ .

Conclusion:

Therefore, the volume of the figure is $28.26{\text{cm}}^3$ .