Question

Need help with two math questions:

Answer 1

Answer:

Part 1) Option B  $1,257\ cm^{3}$

Part 2) The volume of the resulting cone is $50\ cm^{3}$

Step-by-step 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 $h=10-6=4\ cm$

$\frac{1,000\pi }{10}=\frac{x}{4}\\ \\x=1,000\pi *4/10\\ \\x=400\pi \\ \\x=1,257\ cm^{3}$

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

$z^{3}=\frac{x}{y}$

in this problem we have

$z=1/3$

$y=1,350\ cm^{3}$

substitute and solve for x

$(1/3)^{3}=\frac{x}{1,350}$

$(1/27)=\frac{x}{1,350}$

$x=1,350*(1/27)=50\ cm^{3}$

Answer 2

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