Ruby red paint costs $0.50 per square inch. A ball is painted ruby red and costs$100.00 to paint. What is the diameter of the ball?

Jun 9, 2017

$8$ inch

Explanation:

Space area of ball $= 4 \pi {r}^{2}$, where $r =$ radius of ball/sphere

Area of ball * cost of paint per square = total cost of paint,
therefore,
$4 \pi {r}^{2} \cdot 0.5 = 100$

$2 \pi {r}^{2} = 100$

${r}^{2} = \frac{100}{2 \pi}$

 r = sqrt(100 / (2 pi)) = 10/(sqrt(2 pi)

$r = 3.9886 = 4$ inch

therefore, diameter $= 2 \cdot r = 2 \cdot 4 = 8$ inch