Question

A cone of maximum size is carved out from a cube of edge 14 cm. Find the surface area of the remaining solid after the cone is carved out.

Answer 1

here's the answer
volume of remaining solid =volume of cube-volume of square

Answer 2

The cone of maximum size that is carved out from a cube of Edge 14 cm will have base radius 7 cm and height 14 cm.

Slant height of cone,

l = $\sf{\sqrt{ {7}^{2} + ({14})^{2} } cm = \sqrt{245} cm = 7 \sqrt{5} cm}$

Surface area of the cone = CSA + Base area = πrl + $\sf{{\pi \: r}^{2}}$

= $\sf{\pi \:r(l + r) = \frac{22}{7} \times 7(7 \sqrt{5} + 7) {cm}^{2} }$

= $\sf{154( \sqrt{5} + 1) {cm}^{2}}$

Surface area of the remaining solid=

= TSA of the cube + CSA of the cone - Base area of the cone

= $\sf{(6 ({14})^{2} + \frac{22}{7} \times 7 \times 7 \sqrt{5} - \frac{22}{7} \times 7 \times 7) {cm}^{2}}$

= $\sf{(1176 + 154 \sqrt{5} - 154) {cm}^{2} }$

= $\sf{(1022 + 154 \sqrt{5} ) {cm}^{2}}$