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# 3d geometry

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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

#2
+33757
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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
+507
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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
+33757
+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)

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