Question

find the volume the largest right circular cone that can be cut out of a cube whose edge is 9 cm

Answer 1

ANSWER:

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The base of the larges right circular cone will be the circle inscribed in a face of the cube and its height will be equal to an edge of the cube.

Radius of the base of the cone r

$\\ = \frac{9}{2} m$

Height of cone h

$\\ = 9cm$

Now, we will find the volume of the cone using the formula.

$\\ = \frac{1}{3} \pi \: {r}^{2} h........(formula)$

Therefore ,

$\\ volume \: of \: the \: cone = \frac{1}{ 3} \times \frac{22}{7} \times \frac{9}{2} \times \frac{9}{2} \times 9 {cm}^{3} \\ \\ volume \: of \: the \: cone = \frac{11}{7} \times \frac{9}{2} \times \frac{9}{2} \times 9........(cancelling \: 22 \: by \: 2 \: and \: 9 \: by \: 3)$

$\\ volume \: of \: the \: cone \: = \frac{2673}{14} {cm}^{3}$

$volume \: of \: the \: cube = 190.93 {cm}^{3}$

Therefore,

The volume of the cube =190.93cm^3.

Answer 2

Solutions :-

Given :
Edge of cube = 9 cm

Base of the cone will be the circle inscribed in a face of the cube, And the height of the cone is equal to the edge of the cube.


Radius of base of the cone = r = 9/2 = 4.5 cm
Height = h = 9 cm


Find the volume of the right circular cone :-

We know that,
Volume of the right circular cone = ⅓πr²h cu. units
= ⅓ × π × 4.5 × 4.5 × 9 cm³
= 190.93 cm³ (approx.)


Hence,
The volume the largest right circular cone = 190.93 cm³