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

18,000π cm3
18,000 pi cm cubed

2,250π cm3
2,250 pi cm cubed

72,000π cm3
72,000 pi cm cubed

4,500π cm3

1 answer

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 of the cone.

Given that the diameter of the cone is 30 centimeters, we can find the radius:

\[ r = \frac{\text{diameter}}{2} = \frac{30}{2} = 15 \text{ cm} \]

The problem states that the height of the cone is twice the length of the diameter. Since the diameter is 30 cm:

\[ h = 2 \times \text{diameter} = 2 \times 30 = 60 \text{ cm} \]

Now, we can plug the values of \( r \) and \( h \) into the volume formula:

\[ V = \frac{1}{3} \pi (15)^2 (60) \]

Calculating \( r^2 \):

\[ 15^2 = 225 \]

Now substituting that into the equation for volume:

\[ V = \frac{1}{3} \pi (225) (60) \]

Calculating \( 225 \times 60 \):

\[ 225 \times 60 = 13500 \]

Now substitute this back into the volume equation:

\[ V = \frac{1}{3} \pi (13500) \]

Calculating \( \frac{13500}{3} \):

\[ \frac{13500}{3} = 4500 \]

So the volume is:

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

The answer is:

4,500π cm³