Question

the formula for the volume of a cylinder is $v = \pi r^2 h$, where $v$ is the volume, $r$ is the radius, and $h$ is the height. solve the formula for $r$, and then use it to answer the question.
a cylindrical bucket contains 314 cubic inches of water. the height of the water is 4 inches.
what is the radius of the bucket, to the nearest whole number? use 3.14 for $\pi$.
a. 8 inches
b. 6 inches
c. 7 inches
d. 5 inches

Explanation:

Step1: Isolate $r^2$ in formula

Divide both sides by $\pi h$:
$\frac{V}{\pi h} = r^2$

Step2: Solve for $r$

Take square root of both sides:
$r = \sqrt{\frac{V}{\pi h}}$

Step3: Substitute given values

Plug $V=314$, $\pi=3.14$, $h=4$:
$r = \sqrt{\frac{314}{3.14 \times 4}}$

Step4: Calculate denominator first

$3.14 \times 4 = 12.56$

Step5: Compute fraction inside root

$\frac{314}{12.56} = 25$

Step6: Find square root

$\sqrt{25} = 5$

Answer:

D. 5 inches