A carpenter is making a wooden toy (lattu) which is conical in shape and surmounted by a hemisphere. The ratio of the…

Given r: h = $3:4$
Let $r = 3x, h = 4x$
$\therefore r = 3x = 2.1 \Rightarrow x = 0.7$
Hence $h = 2.8$ cm
Volume of wood required to make the toy = Volume of cone + Volume of hemisphere
$= \frac{1}{3} \times \frac{22}{7} \times (2.1)^2 \times 2.8 + \frac{2}{3} \times \frac{22}{7} \times (2.1)^3$
$= 32.34 \text{ cm}^3$
Slant height of cone = $\sqrt{(2.1)^2 + (2.8)^2} = 3.5$ cm
Total Surface Area = CSA of cone + CSA of hemisphere
$= \frac{22}{7} \times 2.1 \times 3.5 + 2 \times \frac{22}{7} \times (2.1)^2$
$= 50.82 \text{ cm}^2$