A toy is in the form of a cone of radius 3.5 cm mounted on a hemisphere of same radius. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

We have VO = 15.5 cm, OA = OO' = 3.5 cm



Let r be the radius of the base of cone and h be the height of conical part of the toy.

Then r = OA = 3.5 cm

h = VO = VO' - OO = (15.5 - 3.5) cm = 12 cm

Also radius of the hemisphere = OA = r = 3.5 cm

l = Slant height, is given by :
\(\Rightarrow l = \sqrt{r^2 + h^2}\)

\(\Rightarrow l = \ \sqrt{OA^2 \ + \ OV^2} \ \)
\( = \ \sqrt{(3.5)^2 \ + \ 12^2} \ \)
\( = \ \sqrt{156.25} \ \)
\( = \ 12.5 \)cm

Total surface area of the toy = Curved surface area of cone + Curved surface area of hemisphere

\(= \ \pi rl \ + \ 2 \pi r^2 \)

\( = \ \pi r(l \ + \ 2r) \ \)
\( = \ \frac{22}{7} \ × \ 3.5 \ × \ 12.5 \ + \ 2 \ × \ 3.5 \)

\( = \ \frac{22}{7} \ × \ 3.5 \ × \ 19.5 \ \)
\( = \ 214.5 \) cm²