Question

these cylinders are similar. find the volume of the smaller cylinder. round to the nearest tenth. 3 cm volume = ? cm³ 5 cm volume = 393 cm³

Explanation:

Step1: Find the ratio of the heights

The ratio of the height of the smaller cylinder to the height of the larger cylinder is $\frac{h_1}{h_2}=\frac{3}{5}$.

Step2: Use the ratio - volume relationship for similar solids

For similar solids, the ratio of their volumes is the cube of the ratio of their corresponding linear dimensions. Let $V_1$ be the volume of the smaller cylinder and $V_2$ be the volume of the larger cylinder. Then $\frac{V_1}{V_2}=(\frac{h_1}{h_2})^3$.
We know $V_2 = 393$ $cm^3$ and $\frac{h_1}{h_2}=\frac{3}{5}$, so $V_1=V_2\times(\frac{3}{5})^3$.

Step3: Calculate the volume of the smaller cylinder

$V_1 = 393\times(\frac{3}{5})^3=393\times\frac{27}{125}=393\times0.216 = 84.888\approx84.9$ $cm^3$.

Answer:

$84.9$ $cm^3$