Find the volume of a right circular cone that has a height of 4.5 ft and a base with a circumference of 12.5 ft. round your answer to the nearest tenth of a cubic foot.

Volume of right circular cone is 18.6 cubic feet.

Solution:

We need to find volume of right circular cone

Given height of right circular cone = 4.5 feet

Given circumference of base of the cone = 12.5 feet

Formula for volume of circular cone =

Where h is height and r is radius of base.

In given information we have height, but do not have radius. So first need to calculate radius of the base from given circumference of base.

Circumference of circle =

Given that circumference =12.5 feet  

On substituting given value of height and calculated value of radius in formula of volume of cone , we get  

Hence volume of right circular cone in consideration is 18.6 cubic feet.

1 number

if we use a graphing calculator, there is only one such number that satisfies the conclusion of the mean value theorem, that is, a number such that

where the right-hand side is the average rate of change of f on the interval [0.5,0.75], which is the slope of the secant line.

in the attached graph, the black line is the secant line which has its slope as the average rate of change of f on [0.5,0.75], while the orange line is the only tangent line to the graph of f in the interval that satisfies the mvt conclusion.