Question

Arrange the cones in order from least volume to greatest volume.

a cone with a diameter of 20 units and a height of 12 units
a cone with a diameter of 18 units and a height of 10 units
a cone with a radius of 10 units and a height of 9 units a cone with a radius of 11 units and a height of 9 units

Answer 1

first one- 20, 12

second one- 18, 10

third one-10, 9

fourth- 11, 9

Explanation:

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Answer 2

`\boxed{\boxed{\text{Volume}_2<\text{Volume}_3<\text{Volume}_4<\text{Volume}_1}}`

Solution-

The volume of the cone is given by,

`\text{Volume}=\pi r^2(h)/(3)`

Where,

r = radius of the base circle,

h = height of the cone.

1. Cone with a diameter of 20 units and a height of 12 units

Here,

Radius = 20/2 = 10 units

Height = 12 units

`\text{Volume}_1=\pi * 10^2* (12)/(3)=400\pi`

2. Cone with a diameter of 18 units and a height of 10 units

Here,

Radius = 18/2 = 9 units

Height = 10 units

`\text{Volume}_2=\pi * 9^2* (10)/(3)=270\pi`

3. Cone with a radius of 10 units and a height of 9 units

Here,

Radius = 10 units

Height = 9 units

`\text{Volume}_3=\pi * 10^2* (9)/(3)=300\pi`

4. Cone with a radius of 11 units and a height of 9 units

Here,

Radius = 11 units

Height = 9 units

`\text{Volume}_4=\pi * 11^2* (9)/(3)=363\pi`

As,

`270\pi <300\pi <363\pi <400\pi`

`\therefore \text{Volume}_2<\text{Volume}_3<\text{Volume}_4<\text{Volume}_1`