Question

Rasheed got a playing top ( lattu) as his birthday present, which surprisingly had no colour on it. He wanted to colour it with his crayons. The top is shaped like a cone surmounted by a hemisphere (see figure below). The entire top is $5cm$ in height and the diameter of the top is $3.5cm.$ Find the area he has to colour (Take $\pi =\frac{22}{7}$).

Answer 1

Given:

Here, Radius of cone $=$ Radius of hemisphere $=r=\frac{3.5}{2}=1.75cm$

height of cone, $h=5-1.75=3.25cm$

slant height of cone, $l=\sqrt{(r{)}^2+(h{)}^2}=\sqrt{(3.25{)}^2+(1.75{)}^2}=\sqrt{13.625}$

$\therefore l=3.6912cm$

The total Surface area of playing top $=$ Curved surface area of cone $+$ curved surface area of hemisphere

$=\pi rl+2\pi r^2$

$=\frac{22}{7}\left(1.75\right)\left(3.6912\right)+2\times \frac{22}{7}(1.75{)}^2$

$=20.3016+19.25$

$=39.5516c{m}^2$

So, Area he has to color $=$ Total surface area of playing top $=39.5516c{m}^2$