Question

From one face of a solid cube of side 14 cm, the largest possible one is carved out. Find the volume and surface area of the remaining solid. (Use π = `22/7`, `sqrt5 = 2.2`)

Answer 1

Side of cube a = 14 cm

Diameter of the largest cone = 14 cm

r = 7 cm, h = 14 cm

Volume of the remaining solid = Volume of the cube − Volume of the cone

= `"(Side)"^3 - 1/3 πr^2h`

= `(14)^3 - 1/3 xx 22/7 xx 7 xx 7 xx 14`

= `2744 - 2156/3`

= `(8232 - 2156)/3`

= `6076/3` cm³

`l = sqrt(r^2 + h^2)`

= `sqrt(7^2 + 14^2)`

= `sqrt(49 + 196)`

= `sqrt245`

= `sqrt(5 xx 49)`

= `7sqrt5`

Surface area of the remaining solid = 6a² − πr² + πrl

= `6 xx 14 xx 14 - 22/7 xx 7^2 + 22/7 xx 7 xx 7sqrt5`

= 1176 − 154 + 344.52

= 1366.52 cm²