Question

page 16 of 16 Volume of a Cone Quick Check 2 of 52 of 5 Items Question Eduardo makes a cone out of clay with a height that’s twice the length of the diameter. The diameter of the cone is 30 centimeters. Find the volume of the cone.(1 point) Responses 4,500π cm3 4,500 pi cm cubed 18,000π cm3 18,000 pi cm cubed 2,250π cm3 2,250 pi cm cubed 72,000π cm3 72,000 pi cm cubed Skip to navigation

Answer 1

To find the volume of the cone, we can use the formula for the volume of a cone:

\[
V = \frac{1}{3} \pi r^2 h
\]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

1. The diameter of the cone is given as 30 cm, so we can find the radius by dividing the diameter by 2:
\[
r = \frac{30}{2} = 15 \text{ cm}
\]

2. The problem states that the height is twice the length of the diameter. Since the diameter is 30 cm, the height is:
\[
h = 2 \times 30 = 60 \text{ cm}
\]

3. Now substitute the values for \( r \) and \( h \) into the volume formula:
\[
V = \frac{1}{3} \pi (15)^2 (60)
\]

4. Calculate \( (15)^2 \):
\[
(15)^2 = 225
\]

5. Now substitute the value back into the volume formula:
\[
V = \frac{1}{3} \pi (225) (60)
\]

6. Multiply \( 225 \) by \( 60 \):
\[
225 \times 60 = 13500
\]

7. Now substitute this value back into the volume expression:
\[
V = \frac{1}{3} \pi (13500)
\]

8. Finally, divide \( 13500 \) by \( 3 \):
\[
V = 4500\pi
\]

Thus, the volume of the cone is:

\[
\text{Volume} = 4500\pi \text{ cm}^3
\]

The correct answer is **4,500π cm³**.