Question

A company makes cones out of solid foam. each cone has a height of 18 inches, and its base has a radius of 3 inches. how much foam is needed to make 25 cones? use 3.14 for it, and do not round your answer.

Answer 1

To make 25 cones each with an 18-inch height and a 3-inch radius base, you would need 4239 cubic inches of foam. This is calculated using the formula for the volume of a cone, V = 1/3πr²h, for one cone and then multiplying the result by 25.

Step-by-step explanation:

To find out how much foam is needed to make 25 cones where each cone has a height of 18 inches and a base radius of 3 inches, we start by calculating the volume of one cone. The formula for the volume of a cone is V = ⅓πr²h, where π (pi) is approximately 3.14, r is the radius, and h is the height.

For one cone, with r = 3 inches and h = 18 inches:

V = ⅓(3.14)(3 inches)²(18 inches)

V = ⅓(3.14)(9 square inches)(18 inches)

V = 3.14 × 9 × 18 ÷ 3

V = 3.14 × 3 × 18

V = 169.56 cubic inches per cone

Then, to find the volume for 25 cones:

Total volume = 169.56 cubic inches/cone × 25 cones

Total volume = 4239 cubic inches

Therefore, you need 4239 cubic inches of foam to make 25 cones.

Answer 2

To calculate the foam needed for 25 cones with a radius of 3 inches and height of 18 inches, we find the volume of one cone using πr²h and then multiply by 25. The total foam needed is 12717 cubic inches.

Step-by-step explanation:

The student's question is related to finding the volume of foam needed to make 25 cones, with each cone having specific measurements. To calculate the volume of a single cone, we use the formula V = πr²h, where π is the constant pi (approximated as 3.14), r is the radius, and h is the height of the cone.

Step 1: Calculate the volume of one cone. The radius is 3 inches and the height is 18 inches. Substitute these values into the formula:
V = πr²h
V = 3.14 × (3 inches)² × 18 inches
V = 3.14 × 9 × 18
V = 3.14 × 162
V = 508.68 cubic inches (volume of one cone).

Step 2: Since the company needs to make 25 cones, multiply the volume of one cone by 25 to get the total volume:
Total volume = 508.68 cubic inches × 25
Total volume = 12717 cubic inches.

Therefore, to make 25 cones, the company would need 12717 cubic inches of foam.