a hemisphere of lead of radius 12cm is cast into a right circular cone of height 54cm. find the radius of the base of the cone.
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Volume of hemisphere = volume of cone
2/3 x π x 7³ = 1/3 x π x r² x 49 (divide both sides by π)
2/3 x 7³ = 1/3 x r² x 49
228 2/3 = 16 1/3 r²
r² = (228 2/3) / (16 1/3)
= 14
r = √14
r = 3.742 cm
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