Question

Find the volume of a cone with a base diameter of 6in and a height of 9in. Use the value 3.14 for π, and do not do any rounding. Be sure to include the correct unit in your answer.

Answer 1

The volume of a cone with a base diameter of 6 inches and a height of 9 inches is 762.42 cubic inches, calculated using the formula V = ⅓πr²h with π approximated by 3.14.

Step-by-step explanation:

To find the volume of a cone with a base diameter of 6 inches and a height of 9 inches, we use the formula for the volume of a cone:

V = ⅓ πr²h

First, we need to find the radius of the base. The radius (r) is half of the diameter, so for a diameter of 6 inches, the radius is 3 inches. Then, plug the radius and the height into the formula with π approximated by 3.14:

V = ⅓(3.14)(3 in)²(9 in)

Next, calculate the radius squared:

(3 in)² = 9 in²

Now substitute this back into the formula:

V = ⅓(3.14)(9 in²)(9 in)

Then multiply the values together:

V = ⅓(3.14)(81 in²)(9 in)

V = ⅓(3.14)(729 in³)

Finally, compute the volume:

V = (3.14)(243 in³)

V = 762.42 in³

Therefore, the volume of the cone is 762.42 cubic inches.