Question

An automobile engineer is revising a design for a conical chamber that was originally specified to be 12 inches long with a circular base diameter of 5.7 inches. In the new design, the chamber is scaled by a factor of 1.5. What is the volume of the revised chamber? Round your answer to two decimal places.

229.96 cubic inches


278.35 cubic inches


344.49 cubic inches


461.19 cubic inches

Answer 1

344.49 cubic inches

Explanation:

Since, the volume of a cone is,

`V=(1)/(3)\pi r^2 h`

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 =
`(5.7)/(2)`=2.85 inches,

`(Radius = (Diameter)/(2))`

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,

`V=(1)/(3)\pi (4.275)^2 (18)`

`=344.487415439\text{ cubic inches }\approx 344.49\text{ cubic inches }`

Third option is correct.

Answer 2

The question is asking to calculate the volume of the revised chamber base on the given data's in your problem, in my further calculation and further understanding about the said problem, I would say that the answer would be 344.49 cubic inches, I hope you are satisfied with my answer and feel free to ask for more