Question

the dairy farm where you work has ordered a cylindrical storage tank for gasoline. steel saddles must be ordered to support the tank above ground. the empty tank is 5.0 feet long, 3.5 feet in diameter, and weighs 250 pounds. the tank will be filled with gasoline weighing 46.81 pounds per cubic foot. about how many pounds will the saddles need to support?
a 1,536
b 2,251
c 2,501
d 3,465
e 9,253

Explanation:

Step1: Find the volume of the cylindrical tank

The formula for the volume of a cylinder is \( V=\pi r^{2}h \). The diameter is 3.5 feet, so the radius \( r = \frac{3.5}{2}=1.75 \) feet, and the height \( h = 5.0 \) feet.
Substitute the values into the formula: \( V=\pi\times(1.75)^{2}\times5 \).
Calculate \( (1.75)^{2}=3.0625 \), then \( V=\pi\times3.0625\times5\approx3.1416\times15.3125\approx48.08 \) cubic feet.

Step2: Calculate the weight of the gasoline

The gasoline weighs 46.81 pounds per cubic foot. So the weight of the gasoline is \( 46.81\times V \).
Substitute \( V\approx48.08 \): \( 46.81\times48.08\approx46.81\times48 = 2246.88 \) (approximate by using 48 for easier calculation, more accurately \( 46.81\times48.08\approx2251 \)).

Step3: Add the weight of the empty tank

The empty tank weighs 250 pounds. So the total weight is the weight of gasoline plus the weight of the tank: \( 2251 + 250=2501 \)? Wait, no, wait. Wait, the previous step: Wait, \( 46.81\times48.08 \): let's recalculate \( V \) more accurately. \( r = 3.5/2 = 1.75 \), \( h = 5 \). \( V=\pi r^{2}h=\pi\times1.75^{2}\times5=\pi\times3.0625\times5 = 15.3125\pi\approx15.3125\times3.14159265\approx48.085 \) cubic feet. Then gasoline weight: \( 46.81\times48.085\approx46.81\times48.085 \). Let's calculate \( 46.81\times48 = 2246.88 \), \( 46.81\times0.085 = 3.97885 \), so total \( 2246.88 + 3.97885 = 2250.85885\approx2251 \). Then add the tank's 250 pounds: \( 2251+250 = 2501 \). Wait, but the option C is 2,501. Wait, maybe I made a mistake. Wait, the problem says "the empty tank is 5.0 feet long, 3.5 feet in diameter, and weighs 250 pounds. The tank will be filled with gasoline weighing 46.81 pounds per cubic foot. About how many pounds will the saddles need to support?" So the total weight is tank weight plus gasoline weight. So gasoline weight is volume times density. Volume of cylinder: \( V=\pi r^{2}h \), \( r = 3.5/2 = 1.75 \), \( h = 5 \). So \( V=\pi(1.75)^25 = \pi3.06255 = 15.3125\pi ≈ 48.08 \) cubic feet. Gasoline weight: 46.81 48.08 ≈ 46.8148 = 2246.88, plus 46.81*0.08≈3.74, so ≈2250.62. Then add tank weight 250: 2250.62 + 250 = 2500.62≈2501. So the total weight is approximately 2501 pounds.

Answer:

C. 2,501