please help me answer this

Question

The weight of a synthetic ball varies directly with the cube of its radius. A ball with a radius of 2 inches weighs 5.20 pounds. Find the weight of a ball of the same material with a 3-inch radius?

Answer 1

The ball's weight varies directly with the cube of its radius. That means weight is a multiple of radius cubed. Since we don't know how many multiples, we use/solve for the constant "k".

 

w = kr³

 

5.2 lbs = k(2 in)³

 

5.2 lb = k(8 in³)

 

(5.2 lb)/(8 in³) = k

 

0.65 lb/in³ = k

 

"k" is a constant, so it doesn't change. You can now use it to solve for any other weight and radius values.

 

w = (0.65 lb/in³)(3 in)³

 

w = (0.65 lb/in³)(27 in³)

 

w = 17.55 lb