Answer:
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Step-by-step explanation:
Given

Required
Determine 
We know that:

This gives:


Collect like terms


Take square roots


By tan identity


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The answer is 15 in³.
The volume of the cone is:

where:
V₁ - the volume of the cone
r₁ - the radius of the cone
h₁ - the height of the cone
The volume of the cylinder is:

where:
V₂ - the volume of the cone
r₂ - the radius of the cone
h₂ - the height of the cone
Since <span>the cone fits exactly inside of the cylinder, they have the same radius and the height:
r</span>₁ = r₂
h₁ = h₂
Also:
V₁ = 5
Now, let's write two volume formulas together:

<span>

</span>
We can include V₂ into V₁:

⇒


Answer:
20 square units
Step-by-step explanation:
You count how many across the parallelogram is (which is 4) and you count how high it is (which is 5). Then you multiply 5×4* which equals 20 square units.
*The reason you do this is because base×hieght=area
Q-2r=4, therefore: q=4+2r.
Plug the value of q into q+r=37, so you get:
4+2r+r=37
3r=37-4=33
3r=33
Therefore: r=11.
q-2r=4, but r=11, so:
q-2(11)=4
q-22=4
Therefore q=26.
Check if the answer is correct using second equation:
q=4+2r=4+2(11)=4+22=26.
So: q=26 and r=11.