Question

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

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Volume\:of\:cone=190.755\:cm^{3}}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{\underline\bold{Given:}} \\ \tt: \implies Edge \: of \: cube = 9 \: cm \\ \\\red{\underline\bold{To \: Find:}} \\ \tt: \implies Volume \: of \: largest \: right \: circular \: cone = ?$

• According to given question :

$\circ \: \text{Base \: diameter \: of \: cone = 9 \: cm} \\ \\ \circ \: \text{Height \: of \: cone = 9 \: cm} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies Volume \: of \: cone = \frac{1}{3} \pi {r}^{2} h \\ \\ \circ \: \text{Putting \: given \: values} \\ \\ \tt: \implies Volume \: of \: cone = \frac{1}{3} \times 3.14 \times {(4.5)}^{2} \times 9 \\ \\ \tt: \implies Volume \: of \: cone = 9.42 \times 20.25 \\ \\ \green{\tt: \implies Volume \: of \: cone = 190.755 {cm}^{3} } \\ \\ \green{\tt\therefore 190.755 \: cm^{3} \: Volume \: of \: cone \: cut \: from \: cube \: of \: edge \: 9 \: cm}$