Solve a problem involving the volume of a cylinder.
Understand the Problem
The question is asking how to solve a problem related to calculating the volume of a cylinder. This involves using the formula for the volume of a cylinder, which is V = πr²h, where r is the radius and h is the height of the cylinder.
Answer
$V = 45\pi$ cubic units, approximately 141.3 cubic units.
Answer for screen readers
The volume of the cylinder is $V = 45\pi$ cubic units, which is approximately 141.3 cubic units.
Steps to Solve
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Identify the variables Determine the radius ($r$) and height ($h$) of the cylinder. For instance, if the radius is 3 units and the height is 5 units, then $r = 3$ and $h = 5$.
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Use the formula for volume The formula for the volume of a cylinder is given by: $$ V = \pi r^2 h $$
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Substitute the values Plug in the values of $r$ and $h$ into the formula. If $r = 3$ and $h = 5$, the equation becomes: $$ V = \pi (3)^2 (5) $$
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Calculate $r^2$ First, calculate $3^2$: $$ 3^2 = 9 $$
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Multiply the values together Now, substitute back into the equation: $$ V = \pi (9)(5) $$
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Simplify the expression Calculate $9 \times 5$: $$ 9 \times 5 = 45 $$
So, now the volume formula looks like this: $$ V = 45\pi $$
- Calculate the numerical value (optional) If you need a numerical approximation, use $\pi \approx 3.14$: $$ V \approx 45 \times 3.14 = 141.3 $$
The volume of the cylinder is $V = 45\pi$ cubic units, which is approximately 141.3 cubic units.
More Information
The formula for the volume of a cylinder is derived from the concept of cross-sectional area multiplied by height. The circle's area contributes to the calculation, which is why the $r^2$ term appears in the formula.
Tips
- Forgetting to square the radius when calculating the area of the base.
- Confusing the dimensions of a cylinder, leading to incorrect radius or height values.
- Not including $\pi$ or using an incorrect approximation for pi.
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