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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]`
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Solution
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
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