In Fig. 16.74, from the top of a solid cone of height 12 cm and base radius 6 cm, a cone of height 4 cm is removed by a plane parallel to the base. Find the total surface area of the remaining solid.

Question

Philoid · Accepted Answer

In triangle ABC and ADE,

DE||BC

So, ∆ABC ~ ∆ADE

⇒ OE = 2cm

let slant height be l

Slant height, l =

⇒ l = 13.42cm

Total surface area of the frustum = πr(r + l)

= π × 6(6 + 13.42)

= 366.21 cm²

Now, for smaller cone:

Slant height, l’ =

⇒ l = 4.472 cm

So, curved surface area of smaller cone = πrl

= π × 2 × 4.472 = 28.11 cm²

Now, total surface area of the remaining frustum = total surface area of the bigger cone – curved surface area of smaller cone + area of base of smaller cone

= 366.21 – 28.11 + π (2)²

= 350.52 cm²