Answer:
C: [tex]V=4840 (2 s.f.)[/tex]
Step-by-step explanation:
The formula for the volume of a cone is:
[tex]V= \frac{1}{3} \pi r^2h[/tex]
Therefore,
[tex]V=\frac{1}{3}\times 3.14\times(\frac{34}{2})^2\times 16\\\\V=4840 (2 s.f.)[/tex]
The volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.
It is defined as a three-dimensional shape in which the base is a circular shape and the diameter of the circle decreases as we move from the circular base to the vertex.
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
Volume can be defined as a three-dimensional space enclosed by an object or thing.
It is given that:
A pile of tailings from a gold dredge is in the shape of a cone.
The diameter of the base is 34 feet and the height is 16 feet.
As we know,
The volume of the cone is given by:
[tex]\rm V=\pi r^2\dfrac{h}{3}[/tex]
r = 34/2 = 17 ft
h = 16 feet
Plug the above values in the formula:
[tex]\rm V=\pi (17)^2\dfrac{16}{3}[/tex]
After solving:
V = 1541.33π cubic feet
Take π = 3.14
V = 1541.33(3.14) cubic feet
V = 4839.78 ≈ 4840 cubic ft
Thus, the volume of the cone is 4840 cubic ft if the diameter of the base is 34 feet and the height is 16 feet option (C) is correct.
Learn more about the cone here:
brainly.com/question/16394302
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