Question
7) Volume of cylinder: \( V=\pi r^{2} \cdot h \), for \( h \)
Ask by Kelley Flynn. in the United States
Feb 04,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
To find the height \( h \) of a cylinder, use the formula:
\[
h = \frac{V}{\pi r^{2}}
\]
Where \( V \) is the volume and \( r \) is the radius.
Solution
To solve the formula for the height \( h \) of a cylinder given the volume \( V \) and radius \( r \), follow these steps:
**Given Formula:**
\[
V = \pi r^{2} \cdot h
\]
**Solving for \( h \):**
1. **Isolate \( h \) on one side of the equation.**
To do this, divide both sides of the equation by \( \pi r^{2} \):
\[
\frac{V}{\pi r^{2}} = h
\]
2. **Rearranged Formula:**
\[
h = \frac{V}{\pi r^{2}}
\]
**Final Formula for Height \( h \):**
\[
h = \frac{V}{\pi r^{2}}
\]
**Example Calculation:**
Suppose you have a cylinder with a volume of \( 50 \) cubic units and a radius of \( 3 \) units. To find the height \( h \):
\[
h = \frac{V}{\pi r^{2}} = \frac{50}{\pi (3)^{2}} = \frac{50}{9\pi} \approx \frac{50}{28.274} \approx 1.767 \text{ units}
\]
So, the height \( h \) is approximately \( 1.767 \) units.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
To solve for height \( h \) in the volume formula \( V = \pi r^{2} \cdot h \), rearrange it to \( h = \frac{V}{\pi r^{2}} \). This means that if you know the volume and the radius of your cylinder, you can easily calculate the height! Just remember to keep the units consistent, whether it’s centimeters or inches! When working with real-world applications, think about how this formula might help in planning for water tanks, soup cans, or even tall cylindrical birthday cakes! For example, if you know how much soup you want to fit into a can, just plug that volume into your equation along with the can's radius to find out how tall it needs to be. It's a deliciously practical problem!
