randallkaila1996
Answered

Remi has two cone-shaped containers with the same diameter. He will place the smaller container inside the larger one. Before he does this, he wants to fill the larger container with water so that it will be completely full but won’t spill when he places the smaller container inside. The diameter of both containers is 12 cm. The height of the smaller container is 6 cm, and the height of the larger container is 18 cm.



What volume of water must Remi put in the large container?

Use 3.14 to approximate pi and express your final answer in hundredths
______ cm3



Answer :

SchwarzschildRadius
So,

All we have to do is subtract the smaller cone's volume from the larger cone's volume.

First, we will use the formula for the volume of a cone to find the volume of the larger cone.
[tex]V_{1} = \frac{1}{3}\pi r^2h[/tex]

Substitute.
[tex]V_{1} = \frac{1}{3}(3.14)(6)^2(18)[/tex]

Simplify exponents.
[tex]V_{1} = \frac{1}{3}(3.14)(36)(18)[/tex]

Multiply.  We will do the fraction last.
[tex]V_{1} = \frac{1}{3}(113.04)(18)[/tex]
[tex]V_{1} = \frac{1}{3}(2034.72)[/tex]
[tex]V_{1} = 678.24\ cm^3[/tex]

Now, use the same formula and procedure to find the volume of the smaller cone.
[tex]V_{2} = \frac{1}{3}\pi r^2h[/tex]

[tex]V_{2} = \frac{1}{3}(3.14)(6)^2(6)[/tex]

Exponents first, and then multiplication, leaving the fraction last.
[tex]V_{2} = \frac{1}{3}(3.14)(36)(6)[/tex]
[tex]V_{2} = \frac{1}{3}(113.04)(6)[/tex]
[tex]V_{2} = \frac{1}{3}(678.24)[/tex]
[tex]V_{2} = 226.08\ cm^3[/tex]

Now, use this formula to find the answer:
[tex]V_{2} - V_{1} = Ans[/tex]

And substitute the now known values.
[tex]678.24 - 226.08 = Ans[/tex]
[tex]452.16\ cm^3 = Ans[/tex]

Remi must put 452.16 cubic centimeters of water into the larger container.

Other Questions