Question

A toy is in the form of a cone of radius 3. 5 cm mounted on a hemisphere of same radius on its circular face. The total height of the toy is 15.5 cm. Find the total surface area of the toy.

Answer 1

Radius of cone = radius of hemisphere, r = 3.5 cm

Height of the cone, h = 15.5 -3.5 = 12 cm

slant height, $l=\sqrt{r^2+h^2}=\sqrt{{3.5}^2+{12}^2}=\sqrt{12.25+144}=\sqrt{156.25}=12.5cm$

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

$=2\pi r^2+\pi rl=\pi r[2r+l]=\frac{22}{7}\times 3.5[2\times 3.5+12.5]=11[7+12.5]=11\times 19.5=214.5c{m}^2$