a diameter of a spherical water tank is 27ft. what is the volume of the tank?

Answer 1

Diameter is equal to twice the radius:

D=2R

So,

27 =2R

27/2=2/2 * R

13.5 = R

Now, volume of a sphere is:

V=4/3 (Pi) R³

V= 4/3 (3.14) (13.5)³

V=4/3 (3.14) (2460)

V=10,301 cu ft.

Answer 2

Formula for volume of a sphere = (4/3)∏r³

Remember that your teacher may want you to have these formulas memorized for your test unless you are given a formula sheet!

So to find the volume, you need r (radius). How do you get the radius from the info in the problem? Remember that the radius of a sphere is half the diameter, just like with a circle.

r = d/2 = 27/2

Extra information just in case you didn't understand that part: A sphere is basically a bunch of circles going from small to big to small diameters stacked and squished together. Think about how if you cut a sphere or a ball at its widest part (the middle), you would see a circle when you look at your cut. The diameter of a sphere runs across the widest part of the sphere (the middle).

Back to the problem: plug your value for r into the volume equation.

V = (4/3)∏r³

V = (4/3)∏(27/2)³

Then you simplify from here. Make sure you know whether your teacher wants a numerical answer with the pi calculated out - you could only do this if you are allowed a calculator.

If you aren't allowed a calculator, your teacher probably wants you to leave ∏ and the fraction in the equation (in its simplest form).

Here is the no-calculator way (except it would be nice to have a calculator for the cubed fraction so I hope you have a calculator lol). Otherwise, just carefully plug this equation into your calculator, following order of operations!

V = (4/3)∏(27/2)³

V = (4/3)∏ (19683 / 8) -> going to multiply these fractions and simplify. It would help to cross cancel.

V = ∏(6561 / 2) = 10305.995

Hope that makes sense!