Question

One specific toy is in the shape of a cone mounted on a cylinder. The total height of the toy is 110 mm and the height of its conical part is 77 mm. The diameters of the base of the conical part is 72 mm and that of the cylindrical part is 40 mm. If its cylindrical part is to be painted red, the surface area need to be painted is

Answer 1

Total height of the cone is 110 mm. & height of its conical part is 77 mm.

∴ Height of its cylindrical part is 

h = 110 - 77 = 33 mm.

Diameter of base of cylindrical part is 

2r = 40 mm

∴ r = 20mm

Since, only cylindrical part is to be painted red.

i.e. curved surface of cylindrical part and one base of cylindrical part is to be painted.

∴ Surface area need to be painted 

= Curved surface area of cylindrical part + one Base area of cylindrical part

= 2 π rh + π r²

= π(2 rh + r²)

= π ( 2 x 20 x 33 + 20²)

= π (1320 + 400)

= 1720π mm²

= \(\frac {1720 π}{100}cm^2\) (1mm = 1/10 cm)

= 17.20 π cm²

= 54.03 cm²