Question

children who have cerebral palsy often use therapy balls to help improve their trunk mobility and strength. a small green therapy ball is filled with 525 cubic inches of air. a silver therapy ball is a dilation of the green therapy ball by a scale factor of 2. about how much air is needed to fill the silver therapy ball? options: 1,050 in³, 4,200 in³, 5,100 in³, 3,150 in³ (with an image of a child using therapy balls)

Explanation:

Step1: Recall volume scale factor

For similar solids, if the scale factor of linear dimensions is \( k \), the volume scale factor is \( k^3 \). Here, \( k = 2 \), so volume scale factor is \( 2^3=8 \).

Step2: Calculate silver ball volume

Green ball volume is \( 525 \, \text{in}^3 \). Silver ball volume \( = 525\times8 = 4200 \, \text{in}^3 \).

Answer:

\( 4200 \, \text{in}^3 \) (corresponding to the option with \( 4,200 \, \text{in}^3 \))