How to compute volume of cylinder?
Understand the Problem
The question is asking for the formula and method to calculate the volume of a cylinder. The volume can typically be computed using the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder.
Answer
$V = \pi r^2 h$ and $V \approx 141.37$ cubic units for $r = 3$ units and $h = 5$ units
Answer for screen readers
The formula for the volume of a cylinder is $V = \pi r^2 h$. If the radius is 3 units and the height is 5 units, the volume approximately equals $141.37$ cubic units.
Steps to Solve
- Identify the formula for the volume of a cylinder
The formula for the volume of a cylinder is given by: $$V = \pi r^2 h$$ where $V$ is the volume, $r$ is the radius of the base, and $h$ is the height of the cylinder.
- Measure the radius and height of the cylinder
Determine the values for the radius (r) and height (h) of the cylinder. These measurements are typically given in the problem or can be measured directly.
- Substitute the values into the formula
Once you have the values for the radius and the height, substitute them into the formula. For example, if the radius is 3 units and the height is 5 units, substitute $r = 3$ and $h = 5$ into the formula: $$ V = \pi (3)^2 (5) $$
- Perform the calculations
Calculate the squared radius: $$ (3)^2 = 9 $$
Next, multiply by the height: $$ 9 \times 5 = 45 $$
Finally, multiply by $\pi$ $$ 45 \pi \approx 141.37 $$ (rounded to two decimal places)
- Write the final answer with units
Express the volume with the appropriate units, which would be cubic units based on the original measurements. For example: $$ V \approx 141.37 , \text{units}^3 $$
The formula for the volume of a cylinder is $V = \pi r^2 h$. If the radius is 3 units and the height is 5 units, the volume approximately equals $141.37$ cubic units.
More Information
The result can be expressed in terms of $\pi$ for an exact answer, such as $45\pi$.
Tips
A common mistake is confusing the radius with the diameter. Ensure you use the radius, which is half the diameter, in the formula. Another mistake is forgetting to square the radius before multiplying by $h$ and $\pi$.