Question

A toy is in the form of a cone mounted on a hemisphere of radius 3.5 cm. The total height of the toy is 15.5 cm. Find the total surface area. [4 MARKS]

Answer 1

Radius of hemisphere = Radius of cone = r = 3.5 = $\frac{7}{2}cm$
For cone: h = 15.5 cm - 3.5 cm = 12 cm
We know that $l^2=r^2+h^2={\left(\frac{7}{2}\right)}^2+(12{)}^2=\frac{49}{4}+144=\frac{625}{4}$
$\therefore$ Slant height of cone, $l=\frac{25}{2}cm$
$\therefore$ Total surface area of the toy = Curved surface area of cone
+ Curved surface area of hemisphere
$=\pi rl+2\pi r^2=\pi r(l+2r)=\frac{22}{7}\times 3.5\times (\frac{25}{2}+7)=11\times \frac{39}{2}=214.5c{m}^2$