20) Find the radius of a cylinder with a volume of $$ 950 \mathrm{in}^{3} $$ and a height of 10 in .

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To find the radius of a cylinder with a given volume and height, we can use the formula for the volume of a cylinder:

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

Given:
- Volume ($$ V $$) = $$ 950 \, \text{in}^3 $$
- Height ($$ h $$) = $$ 10 \, \text{in} $$

We need to find the radius ($$ r $$).

Rearrange the formula to solve for $$ r $$:

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

Substitute the given values into the formula:

$$ r = \sqrt{\frac{950}{\pi \times 10}} $$

Now, we can calculate the radius of the cylinder.
Calculate the value by following steps:
- step0: Calculate:
  $$\sqrt{\frac{950}{\left(\pi \times 10\right)}}$$
- step1: Remove the parentheses:
  $$\sqrt{\frac{950}{\pi \times 10}}$$
- step2: Reduce the fraction:
  $$\sqrt{\frac{95}{\pi }}$$
- step3: Use the properties of radicals:
  $$\frac{\sqrt{95}}{\sqrt{\pi }}$$
- step4: Multiply by the Conjugate:
  $$\frac{\sqrt{95}\times \sqrt{\pi }}{\sqrt{\pi }\times \sqrt{\pi }}$$
- step5: Multiply the numbers:
  $$\frac{\sqrt{95\pi }}{\sqrt{\pi }\times \sqrt{\pi }}$$
- step6: Multiply the numbers:
  $$\frac{\sqrt{95\pi }}{\pi }$$
The radius of the cylinder is approximately $$ 5.49904 \, \text{in} $$.
The radius of the cylinder is approximately $$ 5.5 \, \text{in} $$.

Find the radius of a cylinder with a
volume of and a height of 10 in .

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Find the radius of a cylinder with a volume of and a height of 10 in .