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# hemisphere

0
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A spherical soap bubble lands on a horizontal wet surface and forms a hemisphere of the same volume. Given the radius of the hemisphere is 3 cm, find the radius of the original bubble.

Jan 6, 2021

#1
+218
0

Because of the area ratio of 3d shapes. You have to multiply by cube rt (ratio) so the radius is 3*cubert2

Jan 6, 2021
#2
+112816
-1

If the half bubble were a whole bubble the volume would be double.

so

$$r^3\;\;\alpha\;\; R^3\\ R^3=2r^3\\ 3^3=2r^3\\ 27=2r^3\\ \sqrt[3]{\frac{27}{2}}=r\\ r=\sqrt[3]{\frac{27}{2}}$$

Jan 6, 2021