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, so that it takes up half the total volume of the pot. Find the depth of the salt.

• A. 3
• B. 9
• C. 6
• D. 12

Answer 1

The correct option is C

6

Let the depth of the 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 will be 6 cm deep.