Question

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. [4 MARKS]

Answer 1

Concept: 1 Mark
Application: 3 Marks

Radius of Cone = r = 3.5 cm

Total Height of toy = 15.5 cm

Radius of Hemisphere = radius of cone = r = 3.5 cm

Height of cone = h

$\Rightarrow AO=h$

h = Total height of toy - radius of hemisphere = 15.5 - 3.5 = 12 cm

In $\Delta AOB$, AO = h = Height of cone,

we can apply Pythagoras Theorem to find slant height of the cone.

Slant height of cone
$=AB=l=\sqrt{r^2+h^2}$

$=\sqrt{(3.5{)}^2+(12{)}^2}=\sqrt{12.25+144}$

$=\sqrt{156.25}=12.5cm$

Total surface area of toy

$=$ Surface area of Cone + Surface area of Hemisphere

$=\pi .r.l+2.\pi .r^2$

$=(\frac{22}{7}\times 3.5\times 12.5)+2\times \frac{22}{7}\times 3.5\times 3.5$

$=137.5+77=214.5c{m}^2$