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Answer :
To determine how many gallons a cylindrical pail can hold, follow these detailed steps:
1. Determine the formula for the volume of a cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder,
- and [tex]\( \pi \)[/tex] (pi) is a mathematical constant.
2. Substitute the given values into the formula:
- Radius [tex]\( r = 7 \)[/tex] inches
- Height [tex]\( h = 10 \)[/tex] inches
- [tex]\(\pi = \frac{22}{7}\)[/tex]
So, the volume [tex]\( V \)[/tex] can be calculated as follows:
[tex]\[
V = \left( \frac{22}{7} \right) \times (7)^2 \times 10
\][/tex]
3. Calculate the volume in cubic inches:
[tex]\[
V = \left( \frac{22}{7} \right) \times 49 \times 10
\][/tex]
[tex]\[
V = 22 \times 7 \times 10
\][/tex]
[tex]\[
V = 1540 \text{ cubic inches}
\][/tex]
4. Convert the volume from cubic inches to gallons:
Since there are 231 cubic inches in one gallon, we use the conversion factor:
[tex]\[
V_{\text{gallons}} = \frac{1540 \text{ cubic inches}}{231 \text{ cubic inches per gallon}}
\][/tex]
[tex]\[
V_{\text{gallons}} \approx 6.666666666666667
\][/tex]
5. Round or match the given options:
The value [tex]\( 6.666666666666667 \)[/tex] is approximately equal to 6.7 when rounded.
Given the options:
(A) 9
(B) 4.2
(C) 6.7
(D) 5.1
The correct answer is (C) 6.7.
1. Determine the formula for the volume of a cylinder:
[tex]\[
V = \pi r^2 h
\][/tex]
where:
- [tex]\( V \)[/tex] is the volume,
- [tex]\( r \)[/tex] is the radius of the cylinder,
- [tex]\( h \)[/tex] is the height of the cylinder,
- and [tex]\( \pi \)[/tex] (pi) is a mathematical constant.
2. Substitute the given values into the formula:
- Radius [tex]\( r = 7 \)[/tex] inches
- Height [tex]\( h = 10 \)[/tex] inches
- [tex]\(\pi = \frac{22}{7}\)[/tex]
So, the volume [tex]\( V \)[/tex] can be calculated as follows:
[tex]\[
V = \left( \frac{22}{7} \right) \times (7)^2 \times 10
\][/tex]
3. Calculate the volume in cubic inches:
[tex]\[
V = \left( \frac{22}{7} \right) \times 49 \times 10
\][/tex]
[tex]\[
V = 22 \times 7 \times 10
\][/tex]
[tex]\[
V = 1540 \text{ cubic inches}
\][/tex]
4. Convert the volume from cubic inches to gallons:
Since there are 231 cubic inches in one gallon, we use the conversion factor:
[tex]\[
V_{\text{gallons}} = \frac{1540 \text{ cubic inches}}{231 \text{ cubic inches per gallon}}
\][/tex]
[tex]\[
V_{\text{gallons}} \approx 6.666666666666667
\][/tex]
5. Round or match the given options:
The value [tex]\( 6.666666666666667 \)[/tex] is approximately equal to 6.7 when rounded.
Given the options:
(A) 9
(B) 4.2
(C) 6.7
(D) 5.1
The correct answer is (C) 6.7.
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