Question

Find the volume of the largest right circular conethat can be cut out of a cube whose edge is 18cm

Answer 1

the height of the cone will be equal to the height of the cube as it is cut out from it
hence Height =18
the edge of the cube = the diameter of the cone = 18

$so \: radius = \frac{diameter}{2} \\ = \frac{18}{2} = 9cm \\ \\ \\ \\ volume \: of \:a \: cone \\ \\ = \frac{1}{3} \times \pi {r}^{2} h \\ \\ = \frac{1}{3} \times \ \frac{22}{7} \times {9} \times 9 \times 18 \\ \\ = 1 \times \frac{22}{7} \times 81 \times 6 \\ \\ = \frac{10692}{7} \: or \: 1527.43 \: {cm}^{3}$


thank you