Find the volume (in cm³) of the largest right circular cone that can be cut out from a cube with an edge of 8 cm.
Use $$\pi = \frac{22}{7}$$​

Correct option is B

Given:

Cube edge a = 8 cm

Largest right circular cone inside the cube

Use $$\pi=\dfrac{22}{7}$$​​

Formula Used:

For a square face of side (a), the largest inscribed circle has radius r$$=\dfrac{a}{2}$$​​

Height of cone h = a (apex at center of opposite face).

Cone volume: V$$=\dfrac{1}{3}\pi r^{2}h$$​​

Solution:
r$$=\dfrac{8}{2}=4$$​cm, h = 8 cm.

​$$V=\frac{1}{3}\times\pi\times 4^{2}\times 8 \\ \ \\=\frac{1}{3}\times \pi \times 16 \times 8\\ \ \\=\frac{128}{3}\pi\\ \ \\=\frac{128}{3}\times\frac{22}{7}\\ \ \\=\frac{2816}{21}\text{ cm}^3\\ \ \\= 134\frac2{21}\text{ cm}^3.$$​​