Question

Match each ratio of the volumes of two solids to the pair of solids it represents. 3 : 1 2r : 3h h : 4r 4r : h 4r : 3h 4 : 1

Answer 1

`\begin{gathered} \text{ Volume of a cylinder }=\pi r^2h \\ \\ \text{ Volume of a cone =}(1)/(3)\pi r^2h \\ \\ \text{ Volume of a sphere }=(4)/(3)\pi r^3 \\ \\ \text{ Volume of hemisphere }=(2)/(3)\pi r^3 \end{gathered}`

For 1.

`\frac{\text{ Volume of a cylinder}}{\text{ Volume of a cone}}=(\pi r^2h)/((1)/(3)\pi r^2h)=(1)/((1)/(3))=(3)/(1)=3:1`

For 2.

`\frac{\text{ Volume of a sphere}}{\text{ Volume of a cylinder}}=((4)/(3)\pi r^3)/(\pi r^2h)=(4r)/(3h)=4r:3h`

For 3.