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Question

A toy is in the shape of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the cylindrical part are 13 cm and 5 cm respectively. The radii of the hemispherical and conical parts are the same as that of the cylindrical part. Calculate the surface area of the toy( in cm2) if the height of the conical part is 12 cm.


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Solution

Radius of the hemispherical part = 5 cm.

Curved surface area of the Hemi-spherical part

= 2πr2=[2π×(5)2]cm2=(50π)cm2.

Cylindrical part has radius = 5 cm and height = 13 cm.

Curved surface area of the cylindrical part = 2πrh=(2π×5×13)cm2=(130π)cm2.

Conical part has radius = 5 cm and height = 12 cm.

Its slant height = 52+(12)2=25+144=169=13cm

Curved surface area of the conical part = πrl

= (π x 5 x 13) cm2=(65π)cm2

Hence, the surface area of the toy = (50π + 130π + 65π) cm2 = (245π) cm2 .

= (245×227)cm2=770cm2


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