Question

Please help!!! Very confused on my homework.

The tank is completely filled with water and then drains completely into the pool. The volume of the cylindrical tank is v1=36pir2/1 where r1 is the radius of the tank in feet.
PROBLEM IS ON THE ATTACHMENT!

Answer 1

Step-by-step explanation:

we need to use both equations for the volumes.

the only variables in them are r1 and r2.

when we say both results (volumes) are equal, that means we can create an equation with one formula on one side and the other formula on the other side.

and then we can easily transform the equation into "r1 = ..." or "r2 = ..."

and yes, your teacher made a mistake by hinting to solve for r1 in a. and b. it is r1 in a. and r2 in b.

a.

the goal here is an equation in the form

"r1 = ..."

that means r1 is a function of r2.

36×pi×r1² = 1/2 × 4/3 × pi × r2³ = 4/6 × pi × r2³ =

= 2/3 × pi × r2³

36 × r1² = 2/3 × r2³

r1² = (2/3 / 36) × r2³ = (1/(3×18)) × r2³ = 1/54 × r2³

r1 = sqrt(1/54 × r2³) = 1/3 × sqrt(1/6 × r2³)

b.

the goal here is

"r2 = ..."

again

36×pi×r1² = 2/3 × pi × r2³

36 × r1² = 2/3 × r2³

3×36 × r1² = 2 × r2³

3×18 × r1² = r2³

54 × r1² = r2³

`r2 = \sqrt[3]{54 * {r1}^(2) } = 3 * \sqrt[3]{2 * {r1}^(2) }`

c.

r2 is doubled.

so, we have to go back to our equation of a.

r1 = sqrt(1/54 × r2³).

when r2 is doubled, we get

r1 = sqrt(1/54 × (2×r2)³) = sqrt(1/54 × 8 × r2³) =

= sqrt(8) × sqrt(1/54 × r2³)

so, when r2 doubles, r1 has to grow by the factor of sqrt(8) to keep the equality intact.

Answer 2

To find the inside radius of the coffee mug, use the formula for the volume of a cylinder and the density of water. Rearrange the formula to solve for the height of the coffee, and substitute the given values to find the radius.

Step-by-step explanation:

To find the inside radius of the coffee mug, we can use the formula for the volume of a cylinder:

V = πr²h

Given that the depth of the coffee is 7.50 cm and the volume is 375 g, we need to convert the depth to height in order to solve for the radius. We can use the density of water to find the height:

density = mass/volume

Assuming the density of the coffee is the same as water, we can rearrange the formula to solve for the height:

height = mass/(density × volume) = 375 g/(1 g/cm³ × Πr² × 7.50 cm)

By substituting the given values into the equation, we can solve for the radius of the coffee mug.