b Start by converting the answer from Part A into cubic feet.
A
a About 945.7 inches^3
B
b 4.1 gallons
Practice makes perfect
a To find the volume of an oblique prism, we have to multiply its length, width, and height. In this case the prism is slanted, which means the height is measured on the outside.
Examining the diagram, we see that the height corresponds to one of the legs in a 30-60-90 triangle. In such a triangle, the shorter leg is half the length of the hypotenuse and the longer leg is sqrt(3) times longer than the shorter leg.
Since we have been given the hypotenuse, we can find the leg's length.
The height of the tank is 6sqrt(3) inches. Now we have enough information to determine the volume of the tank.
V=(7)(13)(6sqrt(3))≈ 945.7 in^3
b Now, in order to express the volume in gallons we should first find its volume in cubic feet. To do so, let's recall that there are 12 inches in a foot. This means that to convert from inches to feet we have to use the following conversion factor.
1ft/12in
However, since we want to convert units of volume and not units of length, we need to cube this conversion factor. That way, we will get a conversion factor from in^3 into cubic feet.
(1ft/12in.)^3 ⇔ 1ft^3/12^3in.^3 = 1ft^3/1728in.^3
Multiplying the answer from Part A, 945.6in^3, by this conversion factor will convert it to cubic feet.
Now that we have the volume expressed in cubic feet, we can move to converting it into gallons using the given conversion rate.
7.46gal/1ft^3
Multiplying 0.55ft^3 by this conversion factor will convert it to gallons.
