Question

From a soild cylinder of height 20 cm and diameter 12 cm, a conical cavity of height 8 cm and radius 6 cm is hallowed out. Find the total surface area of the remaining solid.

Answer 1

Given, Height of cylinder h₁ = 20 cm

Radius of cylinder = `12/2` = 6 cm.

Height of the cone (h₂) = 8 cm.

Radius of the cone r = 6 cm.

Total surface area of remaining solid = Curved surface area of cylinder + Curved surface area of cone + Area of the top face of the cylinder

Slant height of the cone (l) = `sqrt("h"_2^2 + "r"^2)`

= `sqrt(8^2 + 6^2)`

= `sqrt(64 + 36)`

= 10 cm.

∴ Curved surface area of cone = πrl

= `22/7 xx 6 xx 10`

= `1320/7` cm²

Curved surface area of cylinder = 2πrh

= `2 xx 22/7 xx 6 xx 20`

= `5280/7` cm²

Area of the top face of the cylinder = πr²

= `22/7 xx 6 xx 6`

= `792/7` cm²

∴ Total surface area of the remaining solid

= `1320/7 + 5280/7 + 792/7`

= `7392/7`

= 1056 cm²