Question

right rectangular prism x is similar to right rectangular prism y. the surface area of right rectangular prism x is 52 square centimeters(cm²) and the surface area of right rectangular prism y 3,328 cm². the volume of right rectangular prism x is 10.5 cubic centimeters (cm³) what is the volume in cm³, of right rectangular prism y?

Explanation:

Step1: Find ratio of surface - areas

Let the ratio of surface - areas $\frac{S_x}{S_y}=\frac{52}{3328}=\frac{1}{64}$. Since for similar solids, if the ratio of side - lengths is $k$, the ratio of surface - areas is $k^{2}$, then $k^{2}=\frac{1}{64}$, so $k = \frac{1}{8}$.

Step2: Find ratio of volumes

For similar solids, the ratio of volumes is $k^{3}$. Since $k=\frac{1}{8}$, the ratio of volumes $\frac{V_x}{V_y}=k^{3}=\frac{1}{512}$.

Step3: Calculate volume of prism y

We know $V_x = 10.5$, and $\frac{V_x}{V_y}=\frac{1}{512}$, so $V_y=10.5\times512 = 5376$.

Answer:

$5376$