Question

cone. The height of the cone is 2 cm and the diameter of the base is 4 cm. the volume of the toy. If a right circular cylinder cir find the difference between the volumes of the cylinder ​

Answer 1

[HeY Mate]

Answer:

Question:

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.

Solution:

Let BPC be the hemisphere and ABC be the cone standing on the base of the hemisphere as shown in the above figure.

The radius BO of the hemisphere (as well as of the cone)

=( ½) × 4 cm = 2 cm.

So, volume of the toy

= (⅔) πr^3 + (⅓) πr2h

3 + (⅓) πr2h= (⅔) × 3.14 × 23 + (⅓)× 3.14 × 22 × 2

3 + (⅓) πr2h= (⅔) × 3.14 × 23 + (⅓)× 3.14 × 22 × 2= 25.12 cm^3

3Now, let the right circular cylinder EFGH circumscribe the given solid

.The radius of the base of the right circular cylinder = HP = BO = 2 cm,

and its height is

EH = AO + OP

= (2 + 2) cm

= 4 cm

So,

the volume required = volume of the right circular cylinder – volume of the toy= (3.14 × 22 × 4 – 25.12) cm^3

3= 25.12 cm^3

Hence, the required difference of the two volumes = 25.12 cm^3.

I Hope It Helps You✌️

Answer 2

Step-by-step explanation:

Volume of cone=1/3×pai×r^2×h

=1/3×22/7×2^2×2

=88/21=4.19 cu cm.

Volume of cylinder=22/7×2^2×2

=88/7=12.29 cu cm.

Difference in their volumes=12.29-4.19

=8.10 cu cm.