Question

A solid toy is in the form of a hemisphere surmounted by a right circular cone. The height of the cone is 4 cm and the diameter of the base is 8 cm. Determine the volume of the toy. If a right circular cylinder circumscribes the toy, find the difference of the volumes of the cylinder and the toytoyy​

Answer 1

Given :

• Height of the cone = 4 cm.
• The diameter of the base = 8 cm.

To find :

• Find the volume of the toy.
• Find the difference of the volumes of the cylinder and the toy.

$\;\large\underbrace{\underline{\sf{Understanding\;the\;Question}}}$

The solid toy is given in the question and that is in the form of right circular cone. Right circular cylinder circumscribes the toy. We have to find the volume of the toy and difference of the volumes of the cylinder of the toy.

Solution :

To find the volume of the toy,

$\implies \bf \dfrac {1}{3} \pi r^2h \ + \ \dfrac {2}{3} \pi r^3$

$\implies \bf \dfrac {1}{3} \pi \times 2^2 \times 2 \ + \ \dfrac {2}{3} \pi \times 2^3$

$\implies \bf 25.12 \ cm^3$

Now,

To find the volume of the cylinder circumscribing,

$\implies \bf \pi r^2h$

$\implies \bf \pi \times 4 \times 4$

$\implies \bf 50.24 \ cm^3$

Difference in volume = $\bf (50.24 \ - \ 25.12) cm^3$

$\implies \bf 25.12 \ cm^3$

$\therefore$ The difference in volume is 25.12 cm³.

Answer 2

SOLUTION:

Given :

Diameter of the base= 4cm

Height of the cone= 2cm

Let BPC is a hemisphere and ABC is a cone.

Radius of hemisphere = Radius of cone

= 4/2 = 2 cm

Volume of toy = volume of hemisphere + volume of cone

Volume of toy = ⅔(πr³) + ⅓(πr²h)

= ⅔(3.14 × 2³) + ⅓(3.14 × 2²× 2)

= ⅔(3.14 × 8) + ⅓(3.14 × 4× 2)

= ⅔(3.14 × 8) + ⅓(3.14 × 8)

=( 3.14 × 8 )(⅔+⅓)

=(25.12) (3/3)

= 25.12 × 1

= 25.12 cm³…………..(1)

Let right circular cylinder EFGH circumscribe the given solid toy.

Radius of cylinder = 2 cm

Height of cylinder= 4 cm

Volume of right circular cylinder = πr²h

= 3.14 × 2² × 4

= 3 .14 × 4 × 4

= 3.14 × 16

= 50.24 cm³

Required volume=  volume of cylinder -  volume of toy

Required volume = 50.24 - 25.12 = 25.12 cm³

Hence, the difference of the volume of the cylinder and toy is 25.12 cm³.

HOPE THIS WILL HELP YOU....