Answer:
344.49 cubic inches
Step-by-step explanation:
Since, the volume of a cone is,
[tex]V=\frac{1}{3}\pi r^2 h[/tex]
Where, r is the radius of the cone,
h is its height.
Since, the diameter of the original conical chamber = 5.7 inches,
So, the radius of the original chamber = [tex]\frac{5.7}{2}[/tex]=2.85 inches,
[tex](Radius = \frac{Diameter}{2})[/tex]
Also, the height of the original chamber = 12 inches,
Given, the chamber is enlarged by the scale factor 1.5,
⇒ The radius of revised chamber, r = 1.5 × 2.85 = 4.275 inches,
And, height of the revised chamber, h = 1.5 × 12 = 18 inches,
Hence, the volume of the revised chamber is,
[tex]V=\frac{1}{3}\pi (4.275)^2 (18)[/tex]
[tex]=344.487415439\text{ cubic inches }\approx 344.49\text{ cubic inches }[/tex]
Third option is correct.
