Question

A wooden toy is in the shape of a cone mounted on a cylinder, as shown in the figure. The total height of the toy is 26 cm, while the height of the conical part is 6 cm. The diameter of the base of the conical part is 5 cm and that of the cylindrical part is 4 cm. The conical part and the cylindrical part are respectively painted red and white. Find the area to be painted by each of these colours. $[Take\pi =22/7.]$

Answer 1

We have,

The base radius of the conical part, $r=\frac{5}{2}=2.5$ cm,

The base radius of the cylindrical part, $R=\frac{4}{2}=2$ cm,

The total height of the toy = 26 cm,

The height of the conical part, h = 6 cm

Also,

The height of the cylindrical part, H = 26 - 6 = 20 cm

And, the slant height of the conical part,
$l=\sqrt{r^2+h^2}=\sqrt{{2.5}^2+6^2}=\sqrt{6.25+36}=\sqrt{42.25}=6.5cm$

Now,

The area to be painted by the red colour = CSA of cone + Area of the base of conical part - Area of the base of the cylindrical part

$=\pi rl+\pi r^2-\pi R^2=\frac{22}{7}\times 2.5\times 6.5+\frac{22}{7}\times 2.5\times 2.5–\frac{22}{7}\times 2\times 2=\frac{22}{7}\times 16.25+\frac{22}{7}\times 6.5–\frac{22}{7}\times 4=\frac{22}{7}\times (16.25+6.5–4)=\frac{22}{7}\times 218.5=58.14c{m}^2$

Also,

The area to be painted by white colour = CSA of cylinder + Area of base of cylinder

$=2\pi RH+\pi R^2=\pi R(2H+R)=\frac{22}{7}\times 2\times (2\times 20+2)=\frac{22}{7}\times 2\times 42=264c{m}^2$