The answers are:
a.)102.02
a.)242.47
The volume of the cone can be expressed as:
![V = \frac{1}{3} \pi r^{2} h](https://tex.z-dn.net/?f=V%20%3D%20%20%20%5Cfrac%7B1%7D%7B3%7D%20%5Cpi%20%20r%5E%7B2%7D%20h)
where:
V - the volume of the cone,
r - the radius of the cone,
h - the height of the cone.
It is given:
h = 12 in
R = 2r = 5.7 in ⇒ r = 5.7 in ÷ 2 = 2.85 in
π = 3.14
Therefore, the volume of the original conical chamber (V₁)
![V = \frac{1}{3} *3.14*(2.85) ^{2} *12 = 3.14*8.1225*4 = 102.02 in^{3}](https://tex.z-dn.net/?f=V%20%3D%20%20%5Cfrac%7B1%7D%7B3%7D%20%2A3.14%2A%282.85%29%20%5E%7B2%7D%20%2A12%20%3D%203.14%2A8.1225%2A4%20%3D%20102.02%20in%5E%7B3%7D%20)
Further, the new chamber is scaled by a factor of 1.5. That means that radius and height of the original chamber are increased 1.5 times:
r₁ = r · 1.5 = 2.85 in · <span>1.5 = 4.275 in
</span>h₁ = h · 1.5 = 12 in · <span>1.5 = 18 in
</span>
The volume of the new chamber is:
![V_1= \frac{1}{3} *3.14*(4.275) ^{2} *18 = 3.14*18.28*6=344.49 in ^{3}](https://tex.z-dn.net/?f=V_1%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2A3.14%2A%284.275%29%20%5E%7B2%7D%20%2A18%20%3D%203.14%2A18.28%2A6%3D344.49%20in%20%5E%7B3%7D%20)
The difference between two chambers is:
V₁ - V = 344.49 - 102.02 = 242.47