# Math

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Charlie is making a toy silo for his children. The silos height is three times it's radius. He is also adding a dome shaped top that is a half sphere. If the total surface area of the silo, when assembled is 100 square inches , what is the height of the silo(i.e., what is the distance from the base of the silo to the tip of the dome shaped top)?

• Math -

I see the surface area as the
circular area of the base + rectangle + 1/2 surface area of the sphere
let the radius be r and the height be h
so we want to measure h+r

given:
" the silo's height i three times its' radius" ---> h+r = 3r
h = 2r

πr^2 + 2πrh + (1/2) 4πr^2 = 100
πr^2 + 2πr(2r) + 2πr^2 = 100
7πr^2 = 100
r^2 = 100/(7π)
r = 2.1324 inches
h = 4.2648 inches

so the height of the toy silo = r+h = 6.397
or appr 6.4 inches

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