Julie gave cone-shaped containers filled with jelly beans to her friends for Easter. The cone-shaped container had a diameter of 6 centimeters and a height of 10 centimeters. Selec... Julie gave cone-shaped containers filled with jelly beans to her friends for Easter. The cone-shaped container had a diameter of 6 centimeters and a height of 10 centimeters. Select the formula you need and use it to find the volume of the container.
Understand the Problem
The question describes a cone-shaped container filled with jelly beans and asks for the volume of the cone. We are given the diameter and height of the container, so we must use the formula for the volume of a cone to find the answer.
Answer
$30\pi \approx 94.2$
Answer for screen readers
$30\pi \approx 94.2$
Steps to Solve
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Find the radius The diameter of the cone is given as 6 cm. The radius is half of the diameter. $$ r = \frac{d}{2} = \frac{6}{2} = 3 \text{ cm} $$
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Use the formula for the volume of a cone The formula for the volume of a cone is $V = \frac{1}{3}\pi r^2 h$, where $r$ is the radius and $h$ is the height. We are given the height $h=10$ cm and calculated the radius $r=3$ cm.
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Plug in the known variables $$ V = \frac{1}{3} \times \pi \times (3)^2 \times 10 $$
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Simplify the equation $$ V = \frac{1}{3} \times \pi \times 9 \times 10 $$ $$ V = \frac{90\pi}{3} $$ $$ V = 30\pi \text{ cm}^3 $$
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Approximate the value of $V$ Using $\pi \approx 3.14$, we can calculate an approximate value for the volume: $$ V \approx 30 \times 3.14 $$ $$ V \approx 94.2 \text{ cm}^3 $$
$30\pi \approx 94.2$
More Information
The volume is expressed in cubic centimeters ($\text{cm}^3$) because it represents a three-dimensional space.
Tips
A common mistake is using the diameter instead of the radius in the volume formula. Remember to always use the radius, which is half the diameter. Another common mistake is forgetting the $\frac{1}{3}$ factor in the cone volume formula.
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