Question

Freddie is buying party hats shaped like a cone. The height of the party hat is 6 inches and the diameter of the base is 4 inches. What is the volume of the party hat in cubic inches? Round to the nearest hundredth. Use 3.14 for pi.

Answer 1

To calculate the volume of the cone-shaped party hat, the formula V = 1/3 π r^2 h is used. With a given diameter of 4 inches and a height of 6 inches, the calculated volume is approximately 25.12 cubic inches, rounded to the nearest hundredth.

Step-by-step explanation:

The student is asking about how to calculate the volume of a cone, which is a topic covered in mathematics, particularly geometry. To find the volume of the party hat, which is cone-shaped, we use the formula:

V =
`(1)/(3) \pi r^2 h`

Where:

• V is the volume,
• \pi is approximately 3.14,
• r is the radius of the cone's base,
• h is the height of the cone.

Since the diameter of the base is given as 4 inches, the radius r is half of that, which is 2 inches. The height h is given as 6 inches. Plugging in the values, we get:

V =
`(1)/(3) \pi (2 in)^2 (6 in)`

=
`(1)/(3) \pi (4 in^2) (6 in)`

=
`(1)/(3) * 3.14 * 4 * 6 in^3`

V = 25.12 in^3

So, the volume of the party hat is approximately 25.12 cubic inches, rounded to the nearest hundredth.