A solid is in the shape of a cone mounted on a hemisphere. The radius of each is 6 cm and the total height of the solid is 14 cm . Find the surface area of the solid.

Correct option is C

Given:
Radius (r) = 6 cm
Total height = 14 cm
Formula Used:
Total Surface Area = Curved Surface Area of cone + Curved Surface Area of hemisphere
TSA = $$\pi r l + 2 \pi r^2$$​​
Solution:
The height of the hemisphere is equal to its radius, so height of hemisphere = 6 cm.
Height of the cone (h) = Total height - radius = 14 - 6 = 8 cm.
Calculate the slant height (l) of the cone:
​$$l = \sqrt{r^2 + h^2} = \sqrt{6^2 + 8^2}$$​​
$$= \sqrt{36 + 64} = \sqrt{100}$$​ = 10 cm.
Surface area of the solid = $$\pi r l + 2\pi r^2$$​​
Surface area = $$(\pi × 6 × 10) + (2 × \pi × 6^2)$$​​
​$$= 60\pi + 72\pi = 132\pi cm^2$$​​
Final Answer
So the correct answer is (c)