jmc

Question

Kadin makes a snowman by stacking snowballs of radius 2 inches, 3 inches, and 5 inches. Assuming all his snowballs are spherical, what is the total volume of snow he uses, in cubic inches? Express your answer in terms of .

Accepted Answer

A sphere with radius r has volume 43 r^3. Thus, the snowballs with radius 2, 3, and 5 inches have volumes 43(2^3), 43(3^3), and 43(5^3) cubic inches respectively. The total volume of snow used is thus align* 43(2^3)+43(3^3)+43(5^3)&=43(2^3+3^3+5^3) &=43(8+27+125) &=6403.align*