Question

these cylinders are similar. find the surface area of the smaller cylinder. round to the nearest tenth.
3 cm
5 cm
surface area = ? cm²
surface area = 236 cm²

Explanation:

Step1: Find the ratio of the heights

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

Step2: Recall the ratio of surface - areas of similar solids

For similar solids, if the ratio of corresponding linear dimensions (like heights) is $a:b$, the ratio of their surface - areas is $a^{2}:b^{2}$. Here, the ratio of the surface - areas of the smaller cylinder to the larger cylinder is $(\frac{3}{5})^{2}=\frac{9}{25}$.

Step3: Set up a proportion to find the surface area of the smaller cylinder

Let $S$ be the surface area of the smaller cylinder. We have the proportion $\frac{S}{236}=\frac{9}{25}$.
Cross - multiply: $25S = 236\times9$.
$25S=2124$.
Solve for $S$: $S=\frac{2124}{25}=84.96$.

Step4: Round to the nearest tenth

Rounding $84.96$ to the nearest tenth gives $85.0$.

Answer:

$85.0$