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 outer surface of a hemisphere. What is the radius of the hemisphere?
+37146 Surface of cube 2 x 2 x 6 = 24 units2
The surface of a sphere with TWICE this surface area (since we are painting only 1/2 of the sphere ) = 4 pi r2 = 48 units2
4 pi r2 = 48
r = sqrt( 48/4pi) = sqrt (12/pi) = 2 sqrt (3/pi)
+592 2x2x6=24
total amount of paint = 24
4$\pi$r$^2$=surface of sphere
2$\pi$r$^2$+$\pi$r$^2$=surface of hemisphere=24
$\pi$r$^2$=8
r$^2$=$\dfrac{8}{\pi}$
r=$\boxed{\frac{2\sqrt2}{\sqrt{\pi}}}$
+37146 Surface of cube 2 x 2 x 6 = 24 units2
The surface of a sphere with TWICE this surface area (since we are painting only 1/2 of the sphere ) = 4 pi r2 = 48 units2
4 pi r2 = 48
r = sqrt( 48/4pi) = sqrt (12/pi) = 2 sqrt (3/pi)
