Question

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Find the volume of the largest right Circular cone that can be cut of a cube whose edge is 21cm.
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Answer 1

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• Edge of the cube = 21cm
• Height of Cone = 21cm
• Radius of cone = 10.5cm
• Volume of cone = 1/3 πr 2h

= 1/3 x 22/7 x 10.5^2 x 21

= 2425.5 cm^3

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Answer 2

Given:

Cube:

The edge of cube is = 21cm

Let us assume the edge or side of cube be 'a'.

Now, a = 21 cm

To find out:

The volume of the largest right Circular cone.

In order to find the volume of right circular cone we first need to calculate radius and height of the cone.

The diameter of the cone= height of the cone= side of the cube.

Diameter of the cone = 21 cm

Radius = Diameter/2 = 21/2 = 10.5 cm

$Volume \: of \: cone \: = \frac{1}{3} \times \pi \times {r}^{2} \times h \\ = \frac{1}{3} \times \frac{22}{7} \times {10.5}^{2} \times 21 \\ \frac{1}{3} \times \frac{22}{7} \times \frac{105}{10} \times \frac{105}{10} \times 21 \\ 22 \times \frac{3}{10} \times \frac{105}{2} \times 7 \\ 22 \times 0.3 \times 52.5 \times 7 \\ 2425.2 {cm}^{3}$

Therefore the volume of the largest right circular cone that can be cut out of a cube of edge 21 cm is 2,425.5 cm^3.