Question

A toy is in the form of a right circular cylinder with a hemisphere on one end and a cone on the other. The height and radius of the base of the cylindrical part are 15 cm and 7 cm respectively. The radius of hemisphere and base of the conical part are same as that of the cylinder. Calculate the volume of the toy, if the height of the cone is 14 cm.

Answer 1

GIVEN :-

For Cylindrical portion ,

• Height (H) = 15cm
• Radius (r) = 7cm

For Hemispherical portion ,

• Radius (r) = 7cm

For Conical portion ,

• Radius (r) = 7cm
• Height (h) = 14cm

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TO FIND :-

• Volume of the toy [ cylinder + hemisphere + cone]

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TO KNOW :-

★ Volume of Cylinder = πr²H

★ Volume of Hemisphere = (2/3)πr³

★ Volume of Cone = (1/3)πr²h

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SOLUTION :-

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Volume of toy = Volume of Cylinder + Volume of hemisphere + Volume of cone

⇒ πr²H + (2/3)πr³ + (1/3)πr²h

Taking πr² common ,

⇒ πr² [ H + (2/3)r + (1/3)h ]

Substituting values we get..

$\\ \implies \sf \: \frac{22}{7} \: {(7)}^{2} \left( 15 + \frac{2}{3} (7) + \frac{1}{3} (11) \: \right) \\ \\ \\ \implies \sf \: 22 \times 7 \left(15 + \frac{14}{3} + \frac{11}{3} \: \right) \\ \\ \\ \implies\sf \: 154 \left( 15 + \frac{25}{3} \right) \\ \\ \\ \implies \sf \: 54 \left( \frac{45 + 25}{3} \right) \\ \\ \\ \implies \sf \: \cancel{54} \times \frac{70}{ \cancel3} \\ \\ \\ \implies \sf \: 18 \times 70 \\ \\ \implies\boxed{ \sf \:1260 {cm}^{3} }$

Hence , volume of toy is 1260cm³.

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MORE FORMULAS :-

★ Volume of cube = edge³

★ Volume of cuboid = l × b × h

★ Volume of sphere = (4/3)πr³

Answer 2

I can solve this answer in just a minute but since some has already Solved it and the answer is VERIFIED so I am not going to waste my time.

I am just answer this question to see who approved this answer as VERIFIED ANSWER.