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Calculating the Volume of a Cone

What is the volume of a cone with a height of 27 cm and a radius of 13 cm? Round your answer to the nearest tenth.

Use the appropriate button on your calculator to complete this problem.

[tex]\[ V = \][/tex]

[tex]\[ \text{cm}^3 \][/tex]


Sagot :

To find the volume of a cone with a given height and radius, we use the formula for the volume of a cone:

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

Where:
- \( V \) is the volume of the cone,
- \( r \) is the radius of the base of the cone,
- \( h \) is the height of the cone, and
- \( \pi \) (pi) is approximately 3.14159.

Given:
- Height \( h = 27 \) cm,
- Radius \( r = 13 \) cm.

Let's go through the steps to find the volume:

1. Square the radius: Calculate \( r^2 \):
[tex]\[ 13^2 = 169 \][/tex]

2. Multiply by the height:
[tex]\[ r^2 \times h = 169 \times 27 = 4563 \][/tex]

3. Multiply by pi (\( \pi \)):
[tex]\[ 4563 \times \pi \approx 4563 \times 3.14159 \approx 14335.087 \][/tex]

4. Divide by 3 to find the volume:
[tex]\[ V = \frac{14335.087}{3} \approx 4778.362 \][/tex]

5. Round to the nearest tenth:
[tex]\[ V \approx 4778.4 \][/tex]

So, the volume of the cone is approximately [tex]\( 4778.4 \text{ cm}^3 \)[/tex].
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