Question

Abigail buys a new salt cellar in the shape of a cylinder topped by a hemisphere. The cylinder has a diameter of 6 cm and a height of 10 cm. She pours the salt into the salt cellar, such that it takes up half the total volume of the pot. Find the depth of the portion occupied by salt.

• A. 3
• B. 9
• C. 6
• D. 12

Answer 1

The correct option is C

6

Let the depth of salt in the pot be 'x'.
Volume of salt cellar = $\pi r^{2}h+\frac{1}{2}\left(\frac{4}{3}\pi r^3\right)$
$\pi \times 3^2\left(10\right)+\frac{1}{2}(\frac{4}{3}\pi \times 3^3)$
=$108\pi$
=$339.29c{m}^3$
So half the total volume= $54\pi or169.65c{m}^3$
We want to find x so that $\pi r^{2}x=169.65$
$\pi (3{)}^{2}x=169.65$
$x=6cm$
So the salt is 6 cm deep.