Question

a conical tank is partially filled with water. the height of the tank is 11 m and the radius of the tank is 5 m. the height of the water is 6 m and the radius of the water is 3 m. how much more water, in cubic meters, could you fit in the tank? use 3.14 for pi and round to the nearest tenth.
a. 56.5 cubic meters
b. 287.8 cubic meters
c. 231.3 cubic meters
d. 344.3 cubic meters

Explanation:

Step1: Recall volume formula for cone

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$.

Step2: Calculate volume of the whole conical tank

Substitute $r = 5$ and $h=11$ into the formula: $V_{total}=\frac{1}{3}\times3.14\times5^{2}\times11=\frac{1}{3}\times3.14\times25\times11=\frac{863.5}{3}\approx287.83$ cubic - meters.

Step3: Calculate volume of the water in the tank

Substitute $r = 3$ and $h = 6$ into the formula: $V_{water}=\frac{1}{3}\times3.14\times3^{2}\times6=\frac{1}{3}\times3.14\times9\times6= 56.52$ cubic - meters.

Step4: Calculate the remaining volume

$V_{remaining}=V_{total}-V_{water}=\frac{863.5}{3}- 56.52=\frac{863.5 - 169.56}{3}=\frac{693.94}{3}\approx231.3$ cubic - meters.

Answer:

C. 231.3 cubic meters