A cone has a height of 14 centimeters and a radius of 7 centimeters. What is its volume? Use π ≈ 3.14 and round your answer to the nearest hundredth.
Understand the Problem
The question asks to find the volume of a cone given its height and radius, and rounded the answer to the nearest hundredth. We can use the formula for the volume of a cone which is V = (1/3) * pi * r^2 * h. Here, we are given the values for height, radius and pi to use.
Answer
$718.11$
Answer for screen readers
$718.11$
Steps to Solve
- Write down the formula for the volume of a cone
The volume $V$ of a cone is given by the formula: $$V = \frac{1}{3} \pi r^2 h$$ where $r$ is the radius and $h$ is the height.
- Substitute the given values into the formula
We are given that $r = 7$ centimeters, $h = 14$ centimeters, and $\pi \approx 3.14$. Substituting these values into the formula, we get: $$V = \frac{1}{3} \times 3.14 \times (7)^2 \times 14$$
- Calculate $r^2$
First, calculate $r^2$: $r^2 = 7^2 = 49$
- Substitute $r^2$ value in the equation
Now, substitute this value back into the volume formula: $$V = \frac{1}{3} \times 3.14 \times 49 \times 14$$
- Multiply the values
Multiply the numbers in the numerator: $3.14 \times 49 \times 14 = 2154.32$ Then substitute it back to the equation: $$V = \frac{2154.32}{3}$$
- Divide by 3
Divide $2154.32$ by 3: $V = 718.106666...$
- Round to the nearest hundredth
Round the result to the nearest hundredth: $V \approx 718.11$
$718.11$
More Information
The volume of the cone is approximately $718.11$ cubic centimeters.
Tips
A common mistake is forgetting to divide by 3 in the formula for the volume of a cone. Another mistake is not rounding to the correct decimal place as specified in the problem. Also, using the diameter instead of the radius is another possible mistake.
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