Chapter 5, Problem 73RE

Solution

To calculate: The volume of the cheese wedge if it is cut out from a wheel.

The volume of the cheese edge is $53.01{\text{cm}}^2$ .

Given information: The shape of a wheel of cheese is a right circular cylinder with diameter $18\text{cm}$ and thickness $5\text{cm}$ . A wedge of cheese is cut from the wheel with central angle $15°$ .

Formula used: The formula to find the area of a circle is $A=\pi r^2$ .

The formula to find the area of regular pentagon is given by $A=\frac{1}{2}\left(\text{perimeter}\right)\left(\text{apothem}\right)$ .

Calculation:

Calculate the radius of the cheese wheel.

  $\begin{array}{c}\text{radius}=\frac{\text{diameter}}{2}\\ =\frac{18\text{cm}}{2}\\ =9\text{cm}\end{array}$

The volume of cheese wheel can be calculated by the formula given as follows.

  $V=\frac{\theta }{360}\cdot \pi \cdot {\left(\text{radius}\right)}^2\cdot \left(\text{thickness}\right)$

Substitute $5$ for thickness, $15°$ for $\theta$ and $9$ for radius in the above formula.

  $\begin{array}{c}V=\frac{15}{360}\cdot \pi \cdot {\left(\text{9}\right)}^2\cdot \left(\text{5}\right)\\ =\frac{15}{40}\cdot \pi \cdot 45\\ =\frac{136\pi }{8}\\ \approx 53.01\end{array}$

Thus, the volume of the cheese edge is $53.01{\text{cm}}^2$ .