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Answer :
Final answer:
The calculated tank volume is approximately 247.36 cubic feet, which is smaller than the claimed capacity of 251 cubic feet. Thus, the answer to whether Mac can win the case against his contractor would be yes, as the installed tank is about 4 cubic feet too small.
Explanation:
The subject of the question is to determine whether the capacity of a cylindrical tank installed by Mac's contractor is indeed what was promised. In this case, the claimed capacity is 1880 gallons or 251 cubic feet.
To verify this, we first need to convert the dimensions of the tank into feet, as all the other measurements are in feet. A height of 2 feet 2 inches is equivalent to 2.1667 feet.
Secondly, we compute the volume of a cylinder using the formula: V=πr²h, where 'r' is the radius and 'h' is the height of the cylinder. Substituting the given values, we get: V=π(6)²(2.1667), which yields a volume of approximately 247.36 cubic feet for the tank.
In comparing this result with the claim of 251 cubic feet, we can conclude that the tank installed by the contractor is indeed smaller than promised. As such, the answer to this question would be: 'Yes, the water tank is about 4 cubic feet too small.'
Learn more about Volume of a Cylinder here:
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The correct option is B. No, the water tank is about 25 cubic feet too large.
To determine whether Mac can win the case against the contractor, we need to calculate the actual volume of the cylindrical tank and compare it to the promised volume of 251 cubic feet.
The volume[tex]\( V \)[/tex]of a cylinder is given by the formula:
[tex]\[ V = \pi r^2 h \][/tex]
where[tex]\( r \)[/tex] is the radius and [tex]\( h \)[/tex] is the height.
Given that the radius[tex]\( r \)[/tex] is 6 feet and the height[tex]\( h \)[/tex] is 2 feet 2 inches, we first convert the height to feet:
[tex]\[ h = 2 + \frac{2}{12} \text{ feet} = 2 + \frac{1}{6} \text{ feet} = 2.1667 \text{ feet} \][/tex]
Now we can calculate the volume:
[tex]\[ V = \pi (6)^2 (2.1667) \][/tex]
[tex]\[ V = \pi (36) (2.1667) \][/tex]
[tex]\[ V = \pi (78.0012) \][/tex]
[tex]\[ V \approx 245.06 \text{ cubic feet} \][/tex]
However, we must note that the actual volume of the tank is larger than this calculation because we rounded down the height from 2 feet 2 inches to 2.1667 feet. To account for the full height, we should use the exact value of[tex]\( \frac{26}{12} \) feet for \( h \).[/tex]
Let's recalculate the volume using the exact height:
[tex]\[ V = \pi (6)^2 \left(\frac{26}{12}\right) \][/tex]
[tex]\[ V = \pi (36) \left(\frac{26}{12}\right) \][/tex]
[tex]\[ V = \pi (78) \][/tex]
[tex]\[ V = 245.2381 \text{ cubic feet} \][/tex]
Now, let's compare the calculated volume to the promised volume of 251 cubic feet:
[tex]\[ \text{Difference} = 251 - 245.2381 \][/tex]
[tex]\[ \text{Difference} \approx 5.7619 \text{ cubic feet} \][/tex]
Since the calculated volume is less than the promised volume, the tank is actually too large, not too small. Therefore, Mac does not have evidence that the tank is too small. The evidence indicates that the tank is about 5.76 cubic feet too large, but since we are rounding to the nearest whole number, we round this to 6 cubic feet.
The final answer is:
B. No, the water tank is about 6 cubic feet too large.
