Question

a sphere has a volume of 20 $cm^3$ if another similar sphere has a radius 3 times larger than the first sphere what is the volume of the larger sphere in $cm^3$ ( volume of a sphere is given by $v = \frac{4}{3}\pi r^3$ ) (1 point) $\square cm^3$

Explanation:

Step1: Recall volume scale factor

For similar solids, the ratio of volumes is the cube of the ratio of corresponding linear dimensions (like radius). If the radius of the larger sphere is \( 3 \) times the smaller one, the volume scale factor is \( 3^3 = 27 \).

Step2: Calculate larger sphere volume

The volume of the smaller sphere is \( 20 \, \text{cm}^3 \). Multiply by the volume scale factor: \( 20\times27 = 540 \).

Answer:

\( 540 \)