8) Volume of cylinder: $$ V=\pi r^{2} \cdot h $$, for $$ r $$

Question

UpStudy AI · Accepted Answer

To solve for the radius $$ r $$ in the volume formula of a cylinder:

$$
V = \pi r^{2} h
$$

follow these steps:

### Step 1: Start with the Volume Formula
$$
V = \pi r^{2} h
$$

### Step 2: Isolate $$ r^{2} $$
To isolate $$ r^{2} $$, divide both sides of the equation by $$ \pi h $$:

$$
\frac{V}{\pi h} = r^{2}
$$

$$
r^{2} = \frac{V}{\pi h}
$$

### Step 3: Solve for $$ r $$
Take the square root of both sides to solve for $$ r $$:

$$
r = \sqrt{ \frac{V}{\pi h} }
$$

### Final Formula
$$
r = \sqrt{ \frac{V}{\pi h} }
$$

### Example Calculation
Suppose you have a cylinder with a volume $$ V = 50 $$ cubic units and a height $$ h = 10 $$ units. To find the radius $$ r $$:

$$
r = \sqrt{ \frac{50}{\pi \times 10} } = \sqrt{ \frac{50}{31.4159} } \approx \sqrt{1.5915} \approx 1.261 \text{ units}
$$

So, the radius of the cylinder is approximately **1.261 units**.

### Summary
To find the radius $$ r $$ of a cylinder when you know its volume $$ V $$ and height $$ h $$, use the formula:

$$
r = \sqrt{ \frac{V}{\pi h} }
$$

This formula allows you to calculate the radius by rearranging the original volume equation to solve for $$ r $$.
To find the radius $$ r $$ of a cylinder, use the formula: $$ r = \sqrt{ \frac{V}{\pi h} } $$ Where: - $$ V $$ is the volume, - $$ h $$ is the height. For example, if $$ V = 50 $$ and $$ h = 10 $$, then: $$ r \approx 1.261 \text{ units} $$

8) Volume of cylinder: \( V=\pi r^{2} \cdot h \), for \( r \)

Real Tutor Solution

Answer

Solution

Bonus Knowledge

Related Questions

Latest Geometry Questions