Question

petroleum is loaded from truck tanks into a large underground storage tank. both the truck tanks and the large underground storage tank are in the shape of right cylinders, but the underground storage has six times the circumference and two times the length of the smaller truck tanks. how many fillings of the smaller truck tanks would be equivalent to a single filling of the large underground storage tank?

12

24

72

108

144

Explanation:

Step1: Recall cylinder volume formula

The volume formula of a cylinder is $V = \pi r^{2}h$. Let the radius of the truck - tank be $r_1$ and its height be $h_1$, so its volume $V_1=\pi r_1^{2}h_1$. The circumference of a circle is $C = 2\pi r$. Given that the circumference of the large - tank is 6 times that of the truck - tank, if $C_1 = 2\pi r_1$ is the circumference of the truck - tank and $C_2=2\pi r_2$ is the circumference of the large - tank, then $2\pi r_2 = 6\times(2\pi r_1)$, so $r_2 = 6r_1$. Also, the height of the large - tank $h_2 = 2h_1$.

Step2: Calculate the volume of the large - tank

The volume of the large underground storage tank $V_2=\pi r_2^{2}h_2$. Substitute $r_2 = 6r_1$ and $h_2 = 2h_1$ into the formula: $V_2=\pi(6r_1)^{2}\times(2h_1)$.

Step3: Simplify the volume of the large - tank

$V_2=\pi\times36r_1^{2}\times2h_1=72\pi r_1^{2}h_1$. Since $V_1=\pi r_1^{2}h_1$, then $\frac{V_2}{V_1}=\frac{72\pi r_1^{2}h_1}{\pi r_1^{2}h_1}=72$.

Answer:

C. 72