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A mound of gravel is shaped like a cone. Circumference at the bottom is 250 feet. The Pile is 35 feet high. how many cubic feet of gravel are in the pile. Round 2 decimal places in each step and round the final answer to the nearest cubic foot

Respuesta :

Kat24lover
Volume of a cone = (1/3) π r² h = (1/3) (Area) (h) Where r = radius of the circular base of the cone , h = height The volume is in units cubed. 
To find the area (π r²) of the circular base from it's circumference: Divide the circumference by 2π: 250/2π = 39.7887 <-----That is the radius. 
Now find the area of the circular base: πr²: π (39.7887)² = 4973.59 
Now find the volume of the cone: (1/3) π r² h: (1/3) (4973.59) (35) = about 58,025.24 ft. cubed

Answer:

The answer is:  58058 cubic feet.

Step-by-step explanation:

It is given that:

A mound of gravel is shaped like a cone. Circumference at the bottom is 250 feet.

This means that the circumference of the circle is: 250 feet

i.e. if r is the radius of the bottom of the cone then

[tex]2\pi r=250\\\\i.e.\\\\r=\dfrac{250}{2\pi}\\\\i.e.\\\\r=\dfrac{125}{\pi}\\\\i.e.\\\\r=39.8089\ feet[/tex]

Now, on rounding to 2 decimal places we have:

                    [tex]r=39.81\ feet[/tex]

Also, the height(h) of the cone is given as:

[tex]h=35\ feet[/tex]

The volume(V) of cone is given by:

[tex]V=\dfrac{1}{3}\times \pi\times r^2\times h\\\\i.e.\\\\V=\dfrac{1}{3}\times 3.14\times (39.81)^2\times 35\\\\i.e.\\\\V=58057.82913\ cubic\ feet[/tex]

which to the nearest foot is given by:

[tex]V=58058\ cubic\ feet[/tex]

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