Question

a hemisphere has a radius of 8.5 inches. what is the radius of a sphere with the same surface area? to the nearest tenth of an inch

Answer 1

\[hemisphereSA=2 \pi r^2\]
\[sphereSA=4 \pi r^2\]

Answer 2

\[hemisphereSA = 2 \pi 8.5^2--->144.5 \pi\]
\[sphereSA=4 \pi r^2=144.5 \pi\]
\[r^2=\frac{ 144.5 \pi }{ 4 \pi }\]
\[r^2=\frac{ 144.5 }{ 4 }\]
\[r=\sqrt{\frac{ 144.5 }{ 4 }}\]
\[r=6.01\]