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Maths-

General

Easy

Question

A Solid consisting of a right circular cone , standing on a hemisphere , is placed upright , in a right circular cylinder , full of water and touches the bottom. Find the volume of the water left in the cylinder having given that the radius of the cylinder is 3 cm and its height is 6 cm, the radius of hemisphere is 2 cm and the height of the cone is 4 cm.Give your answer to the nearest cubic centimetre .

hint Hint:

Volume of cone $equals 1 third pi r squared h$
Volume of cylinder $equals pi r squared h$
Volume of hemisphere $equals 2 over 3 pi r cubed$

The correct answer is: 136cm3

Explanation:

We have given right circular cone , standing on a hemisphere , is placed upright , in a right circular cylinder , full of water and touches the bottom.

We have to find d the volume of the water left in the cylinder having given that the radius of the cylinder is 3cm and its height is 6cm , the radius of hemisphere is 2cm and the height of the cone is 4cm.

Step 1 of 1:
We have
Radius of cylinder 3cm
Height of cylinder 6cm
Radius of hemisphere 2cm
Height of cone 4cm
Volume of the water in the cylinder when it is full
$pi r squared h equals pi cross times 3 cross times 3 cross times 6 equals 54 pi cm cubed$
Volume of water displaced =volume of cone + volume of hemisphere.
$equals 1 third pi r squared h plus 2 over 3 pi r cubed$
$equals 1 third pi r squared left parenthesis h plus 2 r right parenthesis$
$equals 1 third pi 2 squared left parenthesis 4 plus 2 left parenthesis 2 right parenthesis right parenthesis$
$equals 32 over 3 pi cm cubed$
Therefore, volume of water which is left
$equals 54 pi minus 32 over 3 pi$
$equals 130 over 3 pi cm cubed$
= 136.19cm³
= 136cm³

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