Question

callie is sending her nephew a soccer ball for his birthday. she packs the ball in a cubic box that has the same side length as the diameter of the ball. she needs to determine how much space needs to be filled with packing material. (use 3.14 or the (pi) button on your calculator. round all results to the nearest hundredth)

if the sides of the box are 26 cm:

(a) what is the volume of the box? (square) (cm^3)

(b) what is the volume of the ball? (square) (cm^3)

(c) what is the remaining volume of the box that needs to be filled with packing material? (square) (cm^3)

Explanation:

Step1: Calculate box volume

Volume of cube: $V_{box} = s^3$ where $s=26$ cm
$V_{box} = 26^3 = 17576$

Step2: Find ball radius

Radius $r = \frac{d}{2}$, $d=26$ cm
$r = \frac{26}{2} = 13$ cm

Step3: Calculate ball volume

Volume of sphere: $V_{ball} = \frac{4}{3}\pi r^3$
$V_{ball} = \frac{4}{3} \times 3.14 \times 13^3 = \frac{4}{3} \times 3.14 \times 2197 \approx 9202.77$

Step4: Calculate remaining volume

Remaining volume = $V_{box} - V_{ball}$
$17576 - 9202.77 = 8373.23$

Answer:

(a) $17576$ $cm^3$
(b) $9202.77$ $cm^3$
(c) $8373.23$ $cm^3$