Question

A cylinder and a cone have the same diameter: 10 inches. The height of the cylinder is 9 inches. The height of the cone is 18 inches.

What is the relationship between the volume of this cylinder and this cone? Use π = 3.14.

Explain your answer by determining the volume of each and comparing them. Show all your work.

Answer 1

The volume of the cylinder is greater than that of the cone

Explanation :

The volume of a cylinder is given by

• πr^2h

wherein ,π = 3.14,r = radius and h = height.

here, the radius is half the diameter i.e. 10in/2 = 5in and the height is 9in

thus,

• volume_cylinder = 3.14*(5in)^2*9in = 706.5in^3

and

The volume of a cone is given by

• 1/3πr^2h

wherein ,r = 5in and h = 18in

thus,

• volume_cone = 1/3*3.14*(5in)^2*18in = 471in^3

comparing,

• volume_cylinder > volume_cone

thus, the relationship between the two shapes is that the volume of the cylinder is greater than that of the cone.

Answer 2

`\sf V_{\textsf{cylinder}} > V_{\textsf{cone}}`

Explanation:

Let's determine the relationship between the volume of the cylinder and the cone, and calculate the volume of each.

The volume
`\sf V` of a cylinder is given by the formula
`\sf V_{\textsf{cylinder}} = \pi r_{\textsf{cylinder}}^2 h_{\textsf{cylinder}}`, where
`\sf r_{\textsf{cylinder}}` is the radius of the cylinder, and
`\sf h_{\textsf{cylinder}}` is the height.

The volume
`\sf V` of a cone is given by the formula
`\sf V_{\textsf{cone}} = (1)/(3)\pi r_{\textsf{cone}}^2 h_{\textsf{cone}}`, where
`\sf r_{\textsf{cone}}` is the radius of the cone, and
`\sf h_{\textsf{cone}}` is the height.

Given that the diameter of both the cylinder and the cone is 10 inches, the radius of each is
`\sf r = (10)/(2) = 5` inches.

The height of the cylinder is
`\sf h_{\textsf{cylinder}} = 9` inches, and the height of the cone is
`\sf h_{\textsf{cone}} = 18` inches.

Now, let's calculate the volumes:

1. Cylinder:

`\sf V_{\textsf{cylinder}} = \pi * (5 \textsf{ inches})^2 * 9 \textsf{ inches}`

`\sf V_{\textsf{cylinder}} = 3.14 * 25 * 9`

`\sf V_{\textsf{cylinder}} = 706.5 \textsf{ cubic inches}`

2. Cone:

`\sf V_{\textsf{cone}} = (1)/(3)\pi * (5 \textsf{ inches})^2 * 18 \textsf{ inches}`

`\sf V_{\textsf{cone}} = (1)/(3) * 3.14 * 25 * 18`

`\sf V_{\textsf{cone}} = 471 \textsf{ cubic inches}`

Now, let's compare the volumes:

`\sf V_{\textsf{cylinder}} = 706.5 \textsf{ cubic inches}`

`\sf V_{\textsf{cone}} = 471 \textsf{ cubic inches}`

The volume of the cylinder is larger than the volume of the cone.

Mathematically:

`\sf V_{\textsf{cylinder}} > V_{\textsf{cone}}`

Therefore, the relationship between the volume of the cylinder and the cone is that the volume of the cylinder is greater.