The answers are:
a.)102.02
a.)242.47
The volume of the cone can be expressed as:
\(V = \frac{1}{3} \pi r^{2} h\)
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)
\(V = \frac{1}{3} *3.14*(2.85) ^{2} *12 = 3.14*8.1225*4 = 102.02 in^{3}\)
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 · 1.5 = 4.275 in
h₁ = h · 1.5 = 12 in · 1.5 = 18 in
The volume of the new chamber is:
\(V_1= \frac{1}{3} *3.14*(4.275) ^{2} *18 = 3.14*18.28*6=344.49 in ^{3}\)
The difference between two chambers is:
V₁ - V = 344.49 - 102.02 = 242.47
