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 = `5/2` = 2.5 cm,

The base radius of the cylindrical part, R = `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) = 6.5  cm ` 

Now,

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

`= pirl+pir^2-piR^2`

`= 22/7xx2.5xx6.5+22/7xx2.5xx2.5-22/7xx2xx2`

`=22/7xx 16.25 +22/7xx6.25- 22/7xx4`

`= 22/7xx(16.25+6.25-4)`

`=22/7xx18.5`

≈ 58.14 cm²

Also,

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

`= 2piRH + piR^2`

`=piR(2H+R)`

`=22/7xx2xx(2xx20+2)`

`=22/7xx2xx42`

= 264 cm²