SOLUTION;
Case: Comparing Volumes
Given:
A Square-based pyramid and a cylinder
Required: show that the Volume of figure B is 3 times that of figure A
Method:
Step 1: Find we find the Volume of the square-based pyramid.
Volume
[tex]\begin{gathered} V=\frac{1}{3}l\times w\times h \\ V=\frac{1}{3}\times5\pi\times5\pi\times6\pi \\ V=50\pi^3 \end{gathered}[/tex]
Step 2: Find we find the Volume of the Cylinder
[tex]\begin{gathered} V=\pi r^2h \\ V=\pi\times(5\pi)^2\times6 \\ V=\pi\times5\pi\times5\pi\times6 \\ V=150\pi^3 \end{gathered}[/tex]
Step 3:
Dividing the volumes to check if it gives 3
[tex]\begin{gathered} ratio=\frac{V_B}{V_A} \\ ratio=\frac{150\pi^3}{25\pi^3} \\ ratio=3 \end{gathered}[/tex]
Step 4: Since the ratio of the volumes of figure B to A is 3, it means that voume figures B is three times the Volume of figure A.
