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Difficulty: EasyCylindrical Volume Applications

A cylindrical oil storage tank has a diameter of 20 feet20\text{ feet} and a height of 5 feet5\text{ feet}. Using 3.143.14 for π\pi, what is the total volume of the tank?

  1. A
    157 cubic feet157\text{ cubic feet}
  2. B
    314 cubic feet314\text{ cubic feet}
  3. 1,570 cubic feet1,570\text{ cubic feet}Answer
  4. D
    6,280 cubic feet6,280\text{ cubic feet}

Answer

The total volume of the tank is 1,570 cubic feet1,570\text{ cubic feet}.
The correct answer is found by first halving the given diameter (20 feet) to get a radius of 10 feet. The radius is then squared (100) and multiplied by the height (5) and pi (3.14) according to the volume formula V=πr2hV = \pi r^2 h. The calculation 3.14×100×53.14 \times 100 \times 5 equals 1,570 cubic feet1,570\text{ cubic feet}.

Step-by-Step Solution

1
Find the radius of the cylindrical tank.
r=d2=202=10 feetr = \frac{d}{2} = \frac{20}{2} = 10\text{ feet}
The volume formula for a cylinder requires the radius, not the diameter.
2
Set up the volume formula for a cylinder.
V=πr2hV = \pi r^2 h
This is the standard geometric formula to find the volume of any cylinder.
3
Substitute the known values into the formula and solve.
V=3.14×(10)2×5=3.14×100×5=314×5=1,570 cubic feetV = 3.14 \times (10)^2 \times 5 = 3.14 \times 100 \times 5 = 314 \times 5 = 1,570\text{ cubic feet}
Squaring 10 gives 100, which moves the decimal point in 3.14 two places to the right, making the final multiplication straightforward.

Key Concept

Calculating the volume of a cylinder using the radius and height.
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Topics

Cylindrical Volume Applications

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