Joe has exactly enough paint to paint the surface of a cube whose side length is 2. It turns out that this is also exactly enough paint to paint the surface of a sphere. If the volume of this sphere is \(\frac{K \sqrt{6}}{\sqrt{\pi}}\), then what is K?

Lightning Feb 3, 2019

#1**0 **

Area of the cube = 2 x 2 *6 = 24 sq units

VOLUME of a sphere = 4/3 pi r^3 find r from the volume equation given

4/3 pi r^3 = k sqrt 6 / sqrt pi

r^3 = 3/4 * k sqrt 6 / pi sqrt pi

r = cubrt ( 3/4 *k sqrt 6/ (pi sqrt pi )

Surface of a sphere = 4 pi r^2 sub in the r value and equate to 24 sq units

4 pi (cubrt 3/4 *k sqrt 6/ (pi sqrt pi))^2 = 24

Solve fo k = 8

ElectricPavlov Feb 3, 2019