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 615 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. 5 inches
b. 8 inches
c. 7 inches
d. 6 inches

Explanation:

Step1: Rearrange formula for $r$

Start with $V=\pi r^2 h$. Isolate $r^2$:
$$r^2=\frac{V}{\pi h}$$
Take square root:
$$r=\sqrt{\frac{V}{\pi h}}$$

Step2: Substitute given values

$V=615$, $\pi=3.14$, $h=4$:
$$r=\sqrt{\frac{615}{3.14 \times 4}}$$

Step3: Calculate denominator

$$3.14 \times 4 = 12.56$$

Step4: Compute fraction inside root

$$\frac{615}{12.56} \approx 49.0$$

Step5: Find square root

$$r \approx \sqrt{49.0} = 7.0$$
Wait, recalculate precisely: $\frac{615}{12.56} \approx 48.965$, so $\sqrt{48.965} \approx 6.997$, which rounds to 7 inches? No, wait 3.144=12.56, 615/12.56=48.965, square root is ~6.997, which is 7? But wait, let's check 6^23.144=3612.56=452.16, 7^23.144=49*12.56=615.44, which is very close to 615. Oh right, 615.44 is almost 615, so r≈7 inches? Wait no, 615/12.56=48.965, sqrt(48.965)=6.997≈7. So the answer is C. 7 inches.

Correcting the steps:

Step1: Rearrange volume formula for $r$

From $V=\pi r^2 h$, derive:
$$r=\sqrt{\frac{V}{\pi h}}$$

Step2: Plug in given values

Substitute $V=615$, $\pi=3.14$, $h=4$:
$$r=\sqrt{\frac{615}{3.14 \times 4}}$$

Step3: Calculate denominator

$$3.14 \times 4 = 12.56$$

Step4: Compute the fraction

$$\frac{615}{12.56} \approx 48.965$$

Step5: Take square root

$$r \approx \sqrt{48.965} \approx 7.0$$
Round to nearest whole number: $r=7$ inches.

Answer:

D. 6 inches