Question

Two cylinder cans have bases of the same size. The diameter of each is $\mathbf{14}\mathbf{}\mathbf{cm}$. One of the cans is $\mathbf{10}\mathbf{}\mathbf{cm}$ high and the other is $\mathbf{20}\mathbf{}\mathbf{cm}$ high. Find the ratio of their volumes.

Answer 1

Step 1: Given information:

The diameter of both cylinder cans$=14\mathrm{cm}$

The height of the first cylinder can $\left(h_1\right)=10\mathrm{cm}$

The height of the second cylinder can $\left(h_2\right)=20\mathrm{cm}$

Step 2: Calculate the volume of the first cylinder can:

The radius of the can $\left(r\right)=\frac{14}{2}=7\mathrm{cm}$

Volume of first cylinder can $\left(V_1\right)=\mathrm{\pi }{r}^2{h}_1$

$$\begin{gathered} \Rightarrow V_1=\mathrm{\pi }\times 7^2\times 10 \\ \Rightarrow V_1=490\mathrm{\pi }{\mathrm{cm}}^3 \end{gathered}$$

Step 3: Calculate the volume of the second cylinder can.

The radius of the can $\left(r\right)=\frac{14}{2}=7\mathrm{cm}$

Volume of second cylinder can $\left(V_2\right)=\mathrm{\pi }{r}^2{h}_2$

$$\begin{gathered} \Rightarrow V_2=\mathrm{\pi }\times 7^2\times 20 \\ \Rightarrow V_2=980\mathrm{\pi }{\mathrm{cm}}^3 \end{gathered}$$

Step 4: Calculate the ratio of their volumes.

$$\begin{gathered} \therefore \frac{V_1}{V_2}=\frac{490\mathrm{\pi }}{980\mathrm{\pi }} \\ \Rightarrow \frac{V_1}{V_2}=\frac{1}{2} \end{gathered}$$

Hence, the ratio of volumes of both cylinder cans is $1:2$.