The diameter of the base of a cylinder is 14 cm and its height is 15 cm. Find its volume.
Understand the Problem
The question asks to find the volume of a cylinder given its base diameter and height. The diameter is 14 cm, which means the radius is 7 cm, and the height is 15 cm. We need to apply the formula for the volume of a cylinder, V = πr²h.
Answer
The volume of the cylinder is $2310 \text{ cm}^3$.
Answer for screen readers
The volume of the cylinder is $2310 \text{ cm}^3$.
Steps to Solve
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Find the radius The diameter of the cylinder is 14 cm, so the radius $r$ is half of that. $$ r = \frac{14}{2} = 7 \text{ cm} $$
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State the height The height $h$ of the cylinder is given as 15 cm.
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Apply the volume formula The volume $V$ of a cylinder is given by the formula $V = \pi r^2 h$. Using $\pi = \frac{22}{7}$, $r = 7$ cm, and $h = 15$ cm, we can calculate the volume: $$ V = \frac{22}{7} \times (7)^2 \times 15 $$
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Simplify and calculate $$ V = \frac{22}{7} \times 49 \times 15 $$ $$ V = 22 \times 7 \times 15 $$ $$ V = 2310 \text{ cm}^3 $$
The volume of the cylinder is $2310 \text{ cm}^3$.
More Information
The volume is expressed in cubic centimeters ($\text{cm}^3$) because it is a measure of three-dimensional space.
Tips
A common mistake is forgetting to square the radius in the volume formula. Another mistake is using the diameter instead of the radius in the formula. It is also important to include correct units ($\text{cm}^3$ in this problem).
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