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.[Use $\pi=\frac{22 }{7}$ ]

Answer 1

It can be observed that the radius of the conical part and the hemispherical part is same (i.e., 3.5 cm).
Height of hemispherical part = Radius (r) = 3.5 = $\frac{7}{2}$cm
Height of conical part (h) = 15.5 −3.5 = 12 cm

Slant height of cone
$=AB=l=\sqrt{r^2+h^2}$
$=\sqrt{(\frac{7}{2})^{2}+(12)^2}=\sqrt{\frac{49}{4}+144}$
$=\sqrt{\frac{625}{4}}=\frac{25}{2} = 12.5$ cm

Total surface area of toy = CSA of conical part + CSA of hemispherical part
$= \pi rl+2\pi r^2$

$=(\frac{22}{7})×(\frac{7}{2})×(\frac{25}{2})+2×(\frac{22}{7})×(\frac{7}{2})^2$

$= (\frac{275}{2})+77$cm2

$=\frac{ (275+154)}{2}$ cm2

= $\frac{429}{2}$ cm2 = $214.5$ cm2