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 rounded off to the nearest integer.

Answer 1

As per the question we can draw the diagram.

Given:
The radius of the conical part and the hemispherical part is same (i.e., $3.5\text{cm}$)
Height of the hemispherical part, $r=3.5=\frac{7}{2}$
Height of conical part, $h=15.5-3.5=12\text{cm}$

Slant height ($l$) of conical part $l=\sqrt{r^2+h^2}$

= $\sqrt{{\left(\frac{7}{2}\right)}^2+{12}^2}=\sqrt{\frac{49}{4}+144}=\sqrt{\frac{49+576}{4}}$

$=\sqrt{\frac{625}{4}}=\frac{25}{2}$

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

$=\frac{22}{7}\times \frac{7}{2}\times \frac{25}{2}+2\times \frac{22}{7}\times \frac{7}{2}\times \frac{7}{2}$

$=214.7$