Question

Anita buys a new salt cellar in the shape of a cylinder topped by a hemisphere as shown below. 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, marked with x in the diagram.

• 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 = $\pi r^{2}h+\frac{2}{3}\pi r^3$

$=\pi \times 3^2\left(10\right)+(\frac{2}{3}\pi \times 3^3)$

$=\pi [90+18]=108\pi c{m}^3$

So, half the total volume= $54\pi c{m}^3$

We want to find x so that

$\pi r^{2}x=54\pi$

$\Rightarrow \pi (3{)}^{2}x=54\pi$

$\Rightarrow 9x=54$ [Cancelling $\pi$ on either side]

$\Rightarrow x=6$

So, the salt filled will be 6 cm deep.