Question

Find the volume of the largest cone that can be cut out from a cube of edge 14 cm. Also find the surface area of the remaining said $(\sqrt{5}=2.2)$

Answer 1

for the cone to be largest the circular part should be incribed one side of the cube and the height of cone $=$ height of cube.

$\Rightarrow$ height $=14cm$ , radius $=7cm$.

volume $=\frac{1}{3}\pi r^{2}h\Rightarrow \frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 14$

$\Rightarrow \frac{44\times 49}{3}$

$\Rightarrow \frac{2156}{3}c{m}^3$

surface area of remaining solids

$\Rightarrow 5a^2+$ (curved surface area of cone) $+a^2-$ (area of bar cone)

$\Rightarrow 6a^2+\pi r\left(l\right)-\pi a^2$

$\Rightarrow a^2(6-3.14)+\pi \left(\frac{a}{2}\right)\left(\sqrt{a^2+\frac{a^2}{4}}\right)$

$\Rightarrow a^2[6-\pi +\sqrt{5\frac{\pi }{4}}]\Rightarrow 256[6+\frac{\pi (\sqrt{5}-4)}{4}]c{m}^2$

Volume of cone $\frac{2156}{3}c{m}^3$ and surface area of solids $256[6+\frac{\pi (\sqrt{5}-4)}{4}]$

$1174.27c{m}^2$