Math / Geometry

Question $\text{A tank is a vertical cylinder with an inside diameter of 6 ft and a height of 15 ft. What is the weight in pounds of the tank, as in the above case, if the tank itself weighs 20 lbs per ft of height?}$ $\text{A. } 63,424 \text{ lbs}$ $\text{B. } 42,241 \text{ lbs}$ $\text{C. } 16,151 \text{ lbs}$ $\text{D. } 10,605 \text{ lbs}$

Studdy Solution

STEP 1

1. The tank is a vertical cylinder.
2. The inside diameter of the cylinder is $6$ feet.
3. The height of the cylinder is $15$ feet.
4. The tank itself weighs $20$ pounds per foot of height.

STEP 2

1. Calculate the surface area of the cylindrical tank.
2. Determine the weight of the tank based on its height and weight per foot.
3. Verify the calculation with the given options.

STEP 3

Calculate the surface area of the cylindrical tank. Since we are only interested in the weight based on height, we focus on the height-related weight.
The weight of the tank is given by the height multiplied by the weight per foot:
$\text{Weight of the tank} = \text{Height} \times \text{Weight per foot}$

STEP 4

Substitute the given values into the formula:
$\text{Weight of the tank} = 15 \text{ ft} \times 20 \text{ lbs/ft}$

STEP 5

Calculate the weight:
$\text{Weight of the tank} = 15 \text{ ft} \times 20 \text{ lbs/ft}$ $= 300 \text{ lbs}$
Since the calculated weight does not match any of the provided options, it seems there might be a misunderstanding in the problem statement or options. However, based on the given information, the weight of the tank itself is:
$\boxed{300 \text{ lbs}}$

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