A hemisphere of radius 4 cm is cut from a solid sphere of radius 4 cm. What is the remaining volume of the sphere? (Use π ≈ 3.14)
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 134.05 cm3
The hemisphere has the same radius as the sphere, so cutting it out removes half the sphere and leaves the other half: a hemisphere of radius 4 cm. Its volume is half the volume of the sphere.
Remaining volume is that of a hemisphere, \(\displaystyle \frac{2}{3}\pi r^{3}=\frac{2}{3}\times3.14\times4^{3}\)
With \(4^{3}=64\), this is \(\displaystyle \frac{2}{3}\times3.14\times64\), about \(134\,\mathrm{cm^{3}}\)
The nearest option is 134.05 cm3