The total outer surface area of a right circular cone of height 24 cm

The total outer surface area of a right circular cone of height 24 cm with a hemisphere of radius 7 cm upon its base is

  1. 327 π
  2. 307 π
  3. 293 π
  4. 273 π

Answer

The cone and the hemisphere are as shown in the figure:

So, first we need to calculate the slant height (l) of the cone.

Slant height = √(242 + 72) (By Pythagoras theorem)

= √625 = 25 cm

Now, total outer surface area = outer surface area of hemisphere + outer surface area of cone

= πrl + 2πr2, where r = 7 cm and l = 25 cm 

= 25×7π + 2×49π

= (175 + 98) π

= 273 π

The correct option is D.