A spherical water tank holds 15.000ft^3 of water. Find the diameter of the tank ( hint: V=pi/6*D^3
I prefer these kind of formula in terms of the radius.
V = (4/3)π r^3 = 15000
r^3 = 3(15000)/(4π) = 3580.986..
take cube root of both sides
r = 12.299
so the diameter = appr 30.6 ft
or
using your formula:
πD^3/6 = 15000
d^3 = 6(15000)/π = 28647.88976
take cube root of both sides
D = 30.6 , same thing
Well, let's dive right into it, shall we? We have a spherical water tank that's holding 15.000 cubic feet of water. The volume of a sphere can be found using the formula V = (pi/6) * D^3, where V is the volume and D is the diameter.
So, we need to solve for D. To do that, we'll rearrange the formula a bit:
15.000 = (pi/6) * D^3
Now, let's bring in the big guns: some mathematical juggling. We'll multiply both sides of the equation by 6/pi to get rid of that pesky pi/6:
15.000 * (6/pi) = D^3
Now, let's get our friendly cubical root on both sides:
cubrt(15.000 * (6/pi)) = cubrt(D^3)
Taking the cubical root of a number is like trying to find the secret combination to a very tiny, very cubic lock. So, grab your trusty calculator and crunch those numbers to find the cubical root of (15.000 * (6/pi)). And there you have it, my friend, the diameter of the spherical water tank!
To find the diameter of the water tank, we can use the given information about the volume of the tank and the formula V = π/6 * D^3.
Step 1: Rearrange the formula to solve for the diameter.
V = π/6 * D^3
Multiply both sides of the equation by 6/π.
6V/π = D^3
Step 2: Substitute the given volume.
6 * 15,000 ft^3 / π = D^3
Step 3: Simplify the equation.
90,000 ft^3 / π = D^3
Step 4: Take the cube root of both sides to find the diameter.
∛(90,000 ft^3 / π) = D
Using a calculator to evaluate the cube root, we get:
D ≈ 20.08 ft
Therefore, the diameter of the water tank is approximately 20.08 ft.
To find the diameter of the spherical water tank, we can use the given volume and the formula for the volume of a sphere. The formula for the volume of a sphere is V = (4/3)πr^3, where V is the volume and r is the radius of the sphere.
In this case, the volume is given as 15,000 ft^3. However, the given hint provides a different formula for the volume: V = (π/6)D^3, where D is the diameter of the sphere.
Since we want to find the diameter, we need to rearrange the formula to solve for D:
V = (π/6)D^3
Multiply both sides by 6/π:
(6/π)V = D^3
Take the cube root of both sides to find D:
D = (6/π)V^(1/3)
Now we can plug in the given volume:
D = (6/π)(15,000)^(1/3)
Using a calculator, we can evaluate this expression to find the diameter of the tank.