Question

question 1 - 2
a mechanic wants to build an isosceles trapezoidal gas tank for use in a shop. he has sketched out the tank shown below (not to scale). if each cubic foot holds 7.5 gallons, how long would the tank need to be to hold at least 150 gallons of fuel?

Explanation:

Step1: Calculate volume per cubic - foot in gallons

We know that each cubic - foot holds 7.5 gallons.

Step2: Calculate the required volume of the tank

The tank needs to hold at least 150 gallons. Let the volume of the tank be $V$. We use the formula $V=\text{number of gallons}\div\text{gallons per cubic - foot}$. So, $V = \frac{150}{7.5}=20$ cubic - feet.

Step3: Calculate the cross - sectional area of the trapezoid

The area formula for a trapezoid is $A=\frac{(a + b)h}{2}$, where for the given isosceles trapezoid, assume the parallel sides of the trapezoid cross - section are $a = 2$ ft and $b=3$ ft, and height $h = 2$ ft. Then $A=\frac{(2 + 3)\times2}{2}=5$ square feet.

Step4: Calculate the length of the tank

The volume of a prism (the gas tank is a trapezoidal prism) is $V=A\times l$, where $A$ is the cross - sectional area and $l$ is the length. We know $V = 20$ cubic feet and $A = 5$ square feet. Rearranging the formula for $l$, we get $l=\frac{V}{A}$. So, $l=\frac{20}{5}=4$ feet.

Answer:

4 feet