Question

Need help with two math questions:

1. A brand new filled can of chicken broth is 10 cm tall and has a radius of 10 cm. Mishka uses some of the broth to cook and now the broth left in the can is 6 cm high. How much broth did Mishka use?

A) 943 cm³
B) 1257 cm³
C) 1885 cm³
D) 4712 cm³

2. A cone with volume 1350 m³ is dilated by a scale factor of 1/3. What is the volume of the resulting cone?



Thanks to anyone who helps!

Answer 1

Answers: 1:B, 2:450

How-To:

Using the formula for area on the bottom of the can, (pi*r^2) you can then multiply by the amount of height missing, which is 4.

Since it was originally 10, you subtract 4 in order to get 6.

That's how to get 4.

Now, plug in pi*r^2 into a calculator (or if you must work it out, radius, r, is 10, so 10*10 is 100. 100*3.14159265 is 314.159265

Now multiply 314 by the height missing (4) to get approximately 1257.



Now for number 2.
It says it is dilated by a scale factor of 1:3 (from 1350). That means that it was made smaller, (that's what dilated means) by 3 for every 1. So take 1350 and divide it by 3 to get 450

Answer 2

Part 1) Option B
`1,257\ cm^(3)`

Part 2) The volume of the resulting cone is
`50\ cm^(3)`

Explanation:

Part 1)

Find the volume of the can

The volume of the cylinder (can) is equal to

`V=\pi r^(2)h`

we have

`r=10\ cm`

`h=10\ cm`

substitute

`V=\pi (10^(2))(10)=1,000 \pi\ cm^(3)`

Remember that

For
`h=10\ cm` subtends a volume of
`V=1,000 \pi\ cm^(3)`

so

by proportion

Find the volume for
`h=10-6=4\ cm`

`(1,000\pi )/(10)=(x)/(4)\\ \\x=1,000\pi *4/10\\ \\x=400\pi \\ \\x=1,257\ cm^(3)`

Part 2)

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z----> the scale factor

x-----> the volume of the resulting cone

y-----> the volume of the original cone

so

`z^(3)=(x)/(y)`

in this problem we have

`z=1/3`

`y=1,350\ cm^(3)`

substitute and solve for x

`(1/3)^(3)=(x)/(1,350)`

`(1/27)=(x)/(1,350)`

`x=1,350*(1/27)=50\ cm^(3)`