Question

A solid wooden toy is in the form of a hemisphere surrounded by a cone of same radius. The radius of hemisphere is 3.5 cm and the total wood used in the making of toy is 16656 cm3. Find the height of the toy. Also , find the cost of painting the hemispherical part of the toy at the rate of Rs $10perc{m}^2$. Use $\pi =\frac{22}{7}$

Answer 1

Let h be the height of the cone and r be the radius of the base of cone.
The volume of the wooden toy
$=\frac{\pi r^{2}h}{3}+\frac{2}{3}\pi r^3$
$=\frac{1}{3}\times \frac{22}{7}\times 3.5\times 3.5(h+7)$
According to the question,
$\frac{77}{6}(h+7)=\frac{1001}{6}$
$\Rightarrow h=6cm$
The height of the wooden toy = 6 cm + 3.5 cm = 9.5 cm
Now,
Curved surface area of the hemispherical part $=2\times \frac{22}{7}\times 3.5\times 3.5=2\times \frac{22}{7}\times (3.5{)}^2$
Hence, the cost painting the hemispherical part of the toy $=77\times 10$
= Rs 770