Anita buys a new salt cellar in the shape of a cylinder topped by a hemisphere

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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 cellar. Find the depth of the salt, marked with x in the diagram

Options:

A . 3 cm

B . 9 cm

C . 6 cm

D . 12 cm

Answer: Option C
:
C

Let the depth of the salt in the cellar be $^{'} x^{'}$
Volume of = volume of cylinder +
salt cellar   volume of hemisphere

   $= π r^{2} h + \frac{2}{3} π r^{3} = π \times 3^{2} \times 10 + \frac{2}{3} π \times 3^{3} = π [90 + 18] = 108 π {cm}^{3}$
So height $x$ will come on the cylinder.
Half of total volume $= 54 π {cm}^{3}$
$π r^{2} x = 54 π π \times 3^{2} \times x = 54 π 9 x = 54 \Rightarrow x = 6$
$∴$ The salt will be 6 cm deep.

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