Question

Find the volume of the largest right circular cone that can be cut out of a cube whose edge is 21 cm. (use pie R =22 by 7)

Answer 1

answer is 2425.5 cm³

Answer 2

Given,

The dimensions of the cube:

Side of cube = 21 cm

a = 21 cm

The dimensions of the right circular cone:

we know that,

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

d = 21 cm

r = 21/2 cm

r = 10.5 cm

Solution:

$volume \: of \: cone \: = \frac{1}{3} \pi \: {r}^{2} h$

Where,

π = 22/7

r = 10.5 cm

h = 21 cm

$volume \: of \: cone \: = \frac{1}{3} \times \frac{22}{7} \times 10.5 \times 10.5 \times 21$

$volume \: of \: cone \: = \frac{1}{3} \times \frac{22}{7} \times \frac{105}{10} \times \frac{105}{10} \times 21$

$volume \: of \: cone \: = 22 \times \frac{3}{10} \times \frac{105}{2} \times 7$

$volume \: of \: cone \: = 22 \times 0.3 \times 52.5 \times 7$

$volume \: of \: cone \: = 2,425.5 \: {cm}^{3}$

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.