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

Hi there!

Surface area of remaining solid = 6L² - πr² + πrl,
where r and l are the radius and slant height of the cone.

Here,
Diameter of Cone = Edge of Cube = 14 cm

Radius, r = 14/2 = 7 cm

Now,

✨ TSA of Cube:

6(side)²

6 × 14²

6 × 196

1176 cm²


✨ Slant height of Cone:

l = √r² + h²
= √7² + 14²
= √7²(1+2²)

= 7√5 cm

✨ Curved Surface area of Cone:

πrl

22/7 × 7 × 7√5

154√5 cm²

✨ Base area of Cone:

πr²

22/7 × 7 × 7

154 cm²

Therefore,
Surface area of remaining solid = 6L² - πr² + πrl

= 1176 + 154√5 - 154

= 1022 + 154√5

Cheers!