Question

children who have cerebral palsy often use therapy balls to help improve their trunk stability and strength. a small green therapy ball is filled with 525 cubic inches of air. a silver therapy ball represents 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? 3,150 in³ 2,100 in³ 4,200 in³ 1,050 in³

Explanation:

Step1: Recall volume scale factor rule

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

Step2: Calculate volume of silver ball

Volume of green ball is \( 525 \, \text{in}^3 \). Volume of silver ball is \( 525\times8 = 4200 \, \text{in}^3 \).

Answer:

\( 4200 \, \text{in}^3 \) (corresponding to the option "4,200 in³")