Question

these prisms are similar. find the volume of the larger prism in decimal form. 5 m 7 m volume = 50 m³ volume = ? m³

Explanation:

Step1: Find the ratio of side - lengths

The ratio of the side - lengths of the larger prism to the smaller prism is $\frac{7}{5}$.

Step2: Use the volume ratio formula

For similar solids, if the ratio of side - lengths is $a:b$, the ratio of volumes is $a^{3}:b^{3}$. Here, the ratio of volumes is $(\frac{7}{5})^{3}=\frac{7^{3}}{5^{3}}=\frac{343}{125}$.

Step3: Set up a proportion

Let the volume of the larger prism be $V$. We have the proportion $\frac{V}{50}=\frac{343}{125}$.

Step4: Solve for $V$

$V = 50\times\frac{343}{125}=\frac{50\times343}{125}=\frac{17150}{125}=137.2$.

Answer:

$137.2$ m³