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