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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?

 Apr 20, 2021

Best Answer 

 #2
avatar+31353 
+2

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)

 Apr 20, 2021
edited by ElectricPavlov  Apr 20, 2021
 #1
avatar+496 
+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=$\boxed{\frac{2\sqrt2}{\sqrt{\pi}}}$

 Apr 20, 2021
edited by SparklingWater2  Apr 20, 2021
 #2
avatar+31353 
+2
Best Answer

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)

ElectricPavlov Apr 20, 2021
edited by ElectricPavlov  Apr 20, 2021

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