CBSE 10th Class Mathematics

Past year question paper

Year 2020

SET 1, Code Number – 30/5/1

Question Number – 38

hemisphere surmounted by a right circular cone of same radius

cone area and volume problem

# A solid toy is in the form of a hemisphere surmounted by a right circular cone of same radius. The height of the cone is 10 cm and the radius of the base is 7 cm. Determine the volume of the toy. Also find the area of the coloured sheet required to cover the toy. [ Use π = 22/7 and √149 = 12.2

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Volume of the toy = Volume of cone + Volume of hemisphere

Cone: r = 7 cm, h = 10 cm

Hemisphere: r = 7 cm

Volume of toy = [1/3 (πr²h)] + [2/3 (πr³)]

= { 1/3 (πr² [h+ 2r] ) }

= { 1/3 (22 × 7 × 24 ) }

Volume of toy = 1232 cm³

Area of coloured sheet required to cover the toy = CSA of cone + CSA of hemisphere

= πrl + 2πr²

= πr [ l + πr ]

= [22 / 7] × 7 [12.2 + 14]

l² = 10² + 7²

l = 100 + 49

l = √149

l =12.2

= 22 × 26.22

= 576.4 cm²