The formula for the volume of a cylinder is [tex]V = \pi r^2 h[/tex], where [tex]V[/tex] is the volume, [tex]r[/tex] is the radius, and [tex]h[/tex] is the height. Solve the formula for [tex]r[/tex], 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 [tex]\pi[/tex].

A. 8 inches
B. 7 inches
C. 5 inches
D. 6 inches



Answer :

To determine the radius of the cylindrical bucket, we need to solve the formula for the volume of a cylinder. The formula is given by:

[tex]\[ V = \pi r^2 h \][/tex]

where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( \pi \)[/tex] is a constant (approximately 3.14),
- [tex]\( r \)[/tex] is the radius,
- [tex]\( h \)[/tex] is the height.

We are given:
- Volume [tex]\( V = 314 \)[/tex] cubic inches,
- Height [tex]\( h = 4 \)[/tex] inches,
- [tex]\( \pi \approx 3.14 \)[/tex].

First, we need to solve for [tex]\( r \)[/tex], the radius. Start with the original formula:

[tex]\[ 314 = 3.14 \cdot r^2 \cdot 4 \][/tex]

Let's isolate [tex]\( r^2 \)[/tex]:

[tex]\[ r^2 = \frac{314}{3.14 \times 4} \][/tex]

Now, perform the operations inside the fraction:

[tex]\[ 3.14 \times 4 = 12.56 \][/tex]

So,

[tex]\[ r^2 = \frac{314}{12.56} \][/tex]

Next, divide 314 by 12.56:

[tex]\[ r^2 = 25.0 \][/tex]

To find [tex]\( r \)[/tex], take the square root of both sides:

[tex]\[ r = \sqrt{25.0} \][/tex]

[tex]\[ r = 5.0 \][/tex]

Thus, the radius [tex]\( r \)[/tex] is [tex]\( 5.0 \)[/tex] inches.

Since we are asked for the radius to the nearest whole number, we round 5.0 to the nearest whole number:

[tex]\[ r \approx 5 \][/tex]

Therefore, the radius of the bucket, to the nearest whole number, is 5 inches.

The correct answer is:

C. 5 inches