Question

The cylindrical water tank on a semitrailer has a length of 20 feet. The volume of the tank is equal to the product of π, the square of the radius of the tank, and the length of the tank.

Let V represent the volume of the tank, r represent the radius of the tank, and h represent the length of the tank.
1.) Create and equation that could be used to find the volume, V, of the cylindrical tank.
2.) Rewrite the volume formula to create an equation that can be used to calculate the radius, r, of the water tank.
Drag the terms to the correct locations in the equation. Not all terms will be used.
r = √_blank_
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Options: 20V, 400πh, h, 20h, V, 20π
3.) Graph the radical equation that can be used to calculate the radius, r, if the tank.
4.) Suppose the cylindrical water tank has a radius of 12 feet. Use this information and the equation modeling the radius of the tank to complete these statements
The equation modeling this situation has (one, no, two) extraneous solution/s.
The volume of the water tank is about (754, 2,880, 400, 9,048) cubic feet.

Answer 1

The volume of a cylindrical tank is found using the formula V = πr²h. To find the radius r, the formula can be rearranged to r = √(V/(20π)). For a tank with a radius of 12 feet, the volume V is approximately 9,048 cubic feet without extraneous solutions.

Step-by-step explanation:

The volume V of a cylindrical tank is calculated using the formula V = πr²h. To find the radius r, we can rearrange the formula to r = √(×/(πh)). Therefore, given h = 20 feet, the formula becomes r = √(×/(20π)), which simplifies to r = √(V/(20π)). As for the graph, it will show r on the y-axis and V on the x-axis, and will represent the positive branch of a parabola since √(V) is being plotted.

If the tank's radius is 12 feet, using the formula V = π(12²)(20), we find V to be approximately 9,048 cubic feet. Since the calculation is based on an actual measurement for the radius, there are no extraneous solutions.