Question

A toy has a hemispherical base with a conical top attached to it. Radius of the hemisphere = 6 cm. Height of the cone = 8 cm. What is the surface area of the toy?

• A. 132$\pi$ $c{m}^2$
• B. 100$\pi$ $c{m}^2$
• C. 82$\pi$ $c{m}^2$
• D. 60$\pi$ $c{m}^2$

Answer 1

The correct option is A

132$\pi$ $c{m}^2$

The diagram given below can represents the toy.

We can see from the diagram that the bottom circular surface of the cone and the top circular surface of hemisphere come together. These 2 surfaces have been darkened. Once they come together, they become invisible to the eye as observable in the final diagram. In other words these 2 surfaces will not be a part of the surface of the combined body which is the toy.

Hence the surface area of the toy = C.S.A of cone + C.S.A of hemisphere

Cone Radius r = 6 cm, Height h = 8 cm

Slant height l = $\sqrt{r^2+h^2}$ = $\sqrt{6^2+8^2}$ = 10 cm

C.S.A of cone = $\pi$rl = $\pi$ × 6 × 10 = 60$\pi$ $c{m}^2$

C.S.A of hemisphere = 2$\pi$$r^2$ = 2$\pi$$(6{)}^2$ = 72$\pi$ $c{m}^2$

Surface area of the toy = C.S.A of cone + C.S.A of hemisphere

= 72$\pi$ + 60$\pi$

= 132$\pi$ $c{m}^2$