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?

Guest Apr 20, 2021

#2**+2 **

Surface of cube 2 x 2 x 6 = 24 units^{2}

The surface of a sphere with TWICE this surface area (since we are painting only 1/2 of the sphere ) = 4 pi r2 = 48 units^{2}

4 pi r^{2} = 48

r = sqrt( 48/4pi) = sqrt (12/pi) = 2 sqrt (3/pi)

ElectricPavlov Apr 20, 2021

#1**+1 **

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=$\boxed{\frac{2\sqrt2}{\sqrt{\pi}}}$

SparklingWater2 Apr 20, 2021

#2**+2 **

Best Answer

Surface of cube 2 x 2 x 6 = 24 units^{2}

The surface of a sphere with TWICE this surface area (since we are painting only 1/2 of the sphere ) = 4 pi r2 = 48 units^{2}

4 pi r^{2} = 48

r = sqrt( 48/4pi) = sqrt (12/pi) = 2 sqrt (3/pi)

ElectricPavlov Apr 20, 2021