Question

The volume V (in cubic feet) of a right cylinder with a height of 5 feet and radius r (in feet) is given by V=5πr^2. Solve the formula for r. Then find the radius of the cylinder when the volume is 770 cubic feet. Round your answer to the whole number.

Answer 1

Given:

The volume V (in cubic feet) of a right cylinder with a height of 5 feet and radius r (in feet) is given by V=5πr^2.

To find:

Solve the formula for r. Then find the radius of the cylinder when the volume is 770 cubic feet. Round your answer to the whole number.

Solution:

The given equation for the volume of the right cylinder is:

$V = 5 \pi r^2 \:ft^3$

Finding the formula for r:

"r" feet → the radius of the right cylinder

Therefore,

$V = 5 \pi r^2$

$\implies r^2 = \frac{V}{5\pi}$

taking square root on both sides

$\implies \boxed{\bold{r= \sqrt{\frac{V}{5\pi}}}}$ ← formula for r

Finding the radius of the cylinder:

By using the above formula for r and by substituting the value of V = 770 ft³, we get

$r= \sqrt{\frac{770}{5\times \frac{22}{7} }}$

$\implies r= \sqrt{\frac{770\times 7}{5\times 22}}$

$\implies r= \sqrt{\frac{5390}{110}}$

$\implies r= \sqrt{49}$

$\implies \boxed{\bold{r= 7\:ft}}$ ← the radius of the right cylinder

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