6.5.5 Volume of Three Dimensional Shapes, PT3 Practice

Question 13:
Diagram shows a composite solid formed by joining a quarter cylinder and a cuboid which lies on the horizontal plane.


It is given that the height of the cuboid is 9 cm and the volume of the composite solid is  $1002\frac{6}{7}{\text{ cm}}^3.$  
Using  $\pi =\frac{22}{7}$ , calculate the height, in cm, of the quarter cylinder.


Solution:
$\begin{array}{l}V\text{ cuboid}+\frac{1}{4}\left(V\text{ cylinder}\right)=1002\frac{6}{7}\\ \left(6\times 6\times 9\right)+\frac{1}{4}\left(\frac{22}{7}\times {12}^2\times t\right)=\frac{7020}{7}\\ 324+\frac{792}{7}t=\frac{7020}{7}\\ \frac{792}{7}t=\frac{4752}{7}\\ t=6\\ \\ \text{Height of the quarter cylinder}=6\text{ cm}\end{array}$