Question

An wooden toy is made by scooping out a hemisphere of same radius from each end of a solid cylinder. If the height of the cylinder is 10 cm, and its base is of radius 3.5 cm, find the volume of wood in the toy. (Use $(\pi=\frac{22}{7})$).

Answer 1

Answer:

The Volume of wood in the toy = 205.205 cm³.

Step-by-step explanation:

 SOLUTION :  

Given :  

Height of a cylinder = 10 cm

Radius of a cylinder = Radius of hemisphere, r = 3.5 cm

Volume of toy =  Volume of cylinder - 2 x Volume of hemisphere  

= πr²h - 2(⅔ πr³)

= πr²(h - 4/3 r)

= 22/7 × 3.5² (10 - 4/3 × 3.5)

= 22 × 0.5 × 3.5 ( 10 - 14/3)

= 11 × 3.5 (10 - 4.67)

= 38.5 (5.33)

Hence, the Volume of wood in the toy = 205.205 cm³.

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Answer 2

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205.205 cm³.

Step-by-step explanation:

Given,

Height of a cylinder = 10 cm

Let the radius of cylinder be 'r'

then,

Radius of a cylinder

= Radius of hemisphere, r = 3.5 cm

Now,

Volume of toy =  Volume of cylinder - 2(Volume) of hemisphere  

= πr²h - 2(⅔ πr³)

Taking π${r}^{2}$ as common and simplifying,

we get,

= πr²(h - 4/3 r)

putting the value of 'r' and 'h',

we get,

= 22/7 × (3.5)² (10 - 4/3 × 3.5)

= 22 × 0.5 × 3.5 ( 10 - 14/3)

= 11 × 3.5 (10 - 4.67)

= 38.5 (5.33)

Hence,

the Volume of wood in the toy = 205.205 cm³.