Question

Q. A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 2 cm, and the diameter of the base is 4 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference between the volumes of the cylinder and the toy. (Take π = 3.14)
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Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Given :

• The hieght of cone = 2cm
• Diameter at base of cone = 4cm
• Hence, Diameter of Hemisphere = 4cm

To Find :

• The volume of toy
• The volume of cylinder which circumscribe the toy

Formula To Be Applied :

Here, We will use the formula of volume of Hemisphere, Cone and cylinder :

• Volume of Hemisphere = (⅔)πr²
• Volume of cone = πr²h/3
• Volume of cylinder = πr²h

Solution :

Given, Height of cone = 2cm

Base Diameter of cone = 4cm

or, Radius of cone = 2cm

Hence, volume of cone :

$\tt{ \implies volume = \pi {r}^{2} \frac{h}{3} }$

$\tt{ \implies v = 3.14 \times 2 \times 2 \times 2 \frac{2}{3} }$

$\tt{ \implies v = \frac{25.12}{3}}$

$\tt{volume \: of \: cone = 8.37 \bar{3}}$

Hence, The volume cone = 8.373 cm³

__________________________

Given, Diameter of Circle = 4cm

or, Radius = 2cm

Hence, volume of Hemisphere

$\tt{volume \: = \frac{2}{3} \pi {r}^{3} }$

$\tt{ \implies volume = \frac{2}{3} \times 2 \times 2 \times 2 \times 3.14}$

$\tt{ \implies volume = \frac{16}{3} \times 3.14}$

$\tt{ \implies volume = 16.74 \bar{6}}$

Hence, volume of Hemisphere = 16.746 cm³

__________________________

Hence, total volume of toy

= 16.746+8.373

= 25.12 cm³

Hence, Volume of toy = 25.12 cm³

__________________________

Now, we know that if two geometric figurs are circumscribed, they are touching there most of the point without crossing it.

Hence, Hieght of the cylinder = 2+2 cm = 4cm

Radius of cylinder = 2cm

Hence, Volume of cylinder:

$\tt{ volume = \pi {r}^{2} h}$

$\tt{ \implies v = 3.14 \times 2 \times 2 \times 4}$

$\tt{ \implies volume \: of \: cylinder = 50.24 \: {cm}^{3} }$

Hence, Volume of Cylinder = 50.24 cm³

__________________________

Hence, Difference In volume

= Volume of Cylinder-Volume of Toy

= 50.24-25.12

= 25.12 cm³

Hence, Difference In volume = 25.12cm³

Hope it helps you !