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 pi, the square 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.

Part A.

Create an equation that could be used to find the volume, V, of the cylindrical tank.

Part B.

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.

$r = \sqrt{ \frac{?}{?} }$
20h, 20pi, 20V, V, 400(pi)h, i

Part C.

Graph the radical equation that can be used to calculate the radius, r, of the tank. Use lowercase "r" and the uppercase "V" when typing the equation.

Part D.

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 volume of the water tank is about [4,000], [9,048], [754], or [2,880] cubic feet.​

Answer 1

Answer:

Part A

V = π × r² × h

Part B

$r = \sqrt{\dfrac{V}{\pi \times 20} }$

Part C

The graph of the function created with MS Excel is attached

Part D

V ≈ 9,048

Step-by-step explanation:

The length of the cylindrical water tank = 20 feet

The volume of the tank, is given by the product of pi, and the square of the radius and the length of the tank

Where;

V = The volume of the tank

r = The radius of the tank

h = The length of the tank

Part A

The equation that could be used to find the volume of the tank, V, is given as follows;

V = π × r² × h

Part B

The equation that can be used to calculate the radius of the tank r is given by making r the subject of the volume of the cylindrcal tank as follows;

V = π × r² × h

r² = V/(π × h)

r = √(V/(π × 20))

Therefore;

$r = \sqrt{\dfrac{V}{\pi \times h} } = \sqrt{\dfrac{V}{\pi \times 20} }$

Part C

The graph of the equation is given as follows;

r; 0, 3, 6, 9, 12

V; 0, 565.5, 2261.95, 5,089.38, 9047.79

Please find attached the graph of the function created with MS Excel

Part D

When the radius is 12 feet, we get;

V = π × 12² × 20 ≈ 9047.79 ≈ 9,048