anonymous one year ago A cylindrical vase has a diameter of 4 inches. At the bottom of the vase, there are 6 marbles, each of diameter 2 inch. The vase is filled with water up to a height of 8 inches. What is the volume of water in the vase?

1. anonymous

26π in3 16π in3 24π in3 32π in3

2. Valpey

You need to solve for the total volume of the cylinder, then subtract the total volume of the marbles to get the total volume of the water.

3. Valpey

The volume of a cylinder is $$\pi r^2 h$$ (r, the radius is half the diameter) The volume of a sphere is $$\frac{4}{3}\pi r^3$$

4. anonymous

oh ok

5. Valpey

What is the volume of the cylinder in terms of $$\pi$$?

6. anonymous

well pie is 3.14 right?

7. Valpey

It isn't necessary to use the numerical value of pi. You can leave everything in terms of pi. As in $$x = 15\pi$$ or $$y = \frac{2}{3}\pi$$.

8. anonymous

oh ok well idk what the radius is but they tell us the height

9. Valpey

The radius is half the diameter by definition.

10. anonymous

oh ok so the radius would be 2?

11. Valpey

Yes, the radius of the cylinder is 2.

12. anonymous

ok so it would be π2^2*8

13. Valpey

Yes, what is that equal to?

14. anonymous

315.5072?

15. anonymous

@Valpey

16. Valpey

Not quite. Let's still leave it in terms of pi. Let's just resolve $$2^2 * 8$$.

17. Valpey

I think you did $$(\pi*2)^2 * 8$$ when you meant to do $$\pi*(2)^2 * 8$$. Still, we don't actually need to multiply by pi.

18. anonymous

oh ok 2^2*8 is 32

19. anonymous

and yeah thats what i did