Question

Cone A has a height of 3 meters and a radius of 2 meters. Cone B has the same radius, but the height is 6 meters. Calculate the volume of each cone. Which conclusion is correct?
A)
The volume of cone A is twice the volume of cone B.
B)
The volume of cone B is twice the volume of cone A.
C)
The volume of cone B is 4 times the volume of cone A.
D)
The volume of cone B is three times the volume of cone A.

Answer 1

Volume of a cone:

\[V=\frac{ 1 }{ 3 }\pi r ^{2}h\]

For Cone A:

\[V _{A}=\frac{ 1 }{ 3 }\pi r _{A} ^{2}h _{A}\]

For Cone B:

\[V _{B}=\frac{ 1 }{ 3 }\pi r _{B} ^{2}h _{B}\]

But we know: \[r _{A}=r _{B}\] and \[h _{B}=3h _{A}\]

and we can also see that a-d are all ratios, so we plug these into \[V_{B}\] and calculate:

\[\frac{ V _{B} }{ V _{A} }=\frac{ 1/3 \pi r _{a}^{2}(2*h _{a}) }{ 1/3 \pi r _{a}^{2}(h _{a}) }\]

And that gives you what???