Question

The diameter of the circular base of a cylindrical oil tank is 30 feet. The height of the tank is 60 feet. If the depth of the oil in the tank is 40 feet, how many more cubic feet of oil can be added to the tank? (Note: Use 3.14 for .) (Round your answer to the nearest whole number. Only use numerical digits in your answer.)

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Frederik

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67 Answers

First, we need to find the volume of the entire cylindrical oil tank.

The formula to calculate the volume of a cylinder is:

V = \pi r^2 h

We are given the diameter of the circular base (30 feet), so the radius \( r \) is:

r = \frac{30}{2} = 15 \, \text{feet}

The height of the tank is:

h = 60 \, \text{feet}

Now, calculate the volume of the entire tank:

V_{\text{total}} = \pi r^2 h = 3.14 \times 15^2 \times 60

V_{\text{total}} = 3.14 \times 225 \times 60

V_{\text{total}}=42390\,\text{cubic feet}

Next, we need to calculate the volume of oil already in the tank, given its depth (40 feet):

h_{\text{oil}} = 40 \, \text{feet}

The volume of the oil is:

V_{\text{oil}} = \pi r^2 h_{\text{oil}} = 3.14 \times 15^2 \times 40

V_{\text{oil}} = 3.14 \times 225 \times 40

V_{\text{oil}} = 28260 \, \text{cubic feet}

Finally, subtract the volume of oil from the total volume to find the remaining capacity:

V_{\text{remaining}} = V_{\text{total}} - V_{\text{oil}}

V_{\text{remaining}}=42390-28260

V_{\text{remaining}}=14130\,\text{cubic feet}

To ensure rounding to the nearest whole number, we get:

14130

Thus, the remaining capacity for more oil is:

14130\,\text{cubic feet}

The formula to calculate the volume of a cylinder is:

We are given the diameter of the circular base (30 feet), so the radius \( r \) is:

The height of the tank is:

Now, calculate the volume of the entire tank:

Next, we need to calculate the volume of oil already in the tank, given its depth (40 feet):

The volume of the oil is:

Finally, subtract the volume of oil from the total volume to find the remaining capacity:

To ensure rounding to the nearest whole number, we get:

Thus, the remaining capacity for more oil is:

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