What is the volume of a cone with a diameter of 20 cm and a height of 15 cm. Use 3.14 for pi

1 answer

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

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

where:

  • \( V \) is the volume,
  • \( r \) is the radius,
  • \( h \) is the height,
  • \( \pi \) is a constant (approximately 3.14 in this case).

First, we need to find the radius. The diameter of the cone is given as 20 cm, so the radius \( r \) is:

\[ r = \frac{\text{diameter}}{2} = \frac{20 , \text{cm}}{2} = 10 , \text{cm} \]

Next, we can substitute the values into the volume formula. The height \( h \) is provided as 15 cm.

Now, plugging in the values:

\[ V = \frac{1}{3} \times 3.14 \times (10 , \text{cm})^2 \times 15 , \text{cm \]

Calculating \( (10 , \text{cm})^2 \):

\[ (10 , \text{cm})^2 = 100 , \text{cm}^2 \]

Now, substituting this back into the volume formula:

\[ V = \frac{1}{3} \times 3.14 \times 100 , \text{cm}^2 \times 15 , \text{cm} \]

Calculating the total:

\[ V = \frac{1}{3} \times 3.14 \times 1500 , \text{cm}^3 \]

Calculating \( 3.14 \times 1500 \):

\[ 3.14 \times 1500 = 4710 \]

Now, divide by 3:

\[ V = \frac{4710}{3} \approx 1570 , \text{cm}^3 \]

So, the volume of the cone is approximately 1570 cm³.