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A cone has a height of 5 inches and a circumference
of 56.52 inches.
Which measurement is closest to the volume of the
cone in cubic inches? Use 3.14 for π .
A 1695.6
B 1271.7
C 887.36
D 423.9

Respuesta :

The volume of a cone is found by saying:
V = 1/3 * pi * r^2 * h 

The circumference is equal to
C = 2*pi*r

So the radius of the cone is
r = C/2pi

So the volume of this cone is
V=1/3 * pi * h * (C/2pi)^2 = 1/12 * h * C^2/pi = 423.9
calculista

Answer:

Option D [tex]423.9\ in^{3}[/tex]

Step-by-step explanation:

we know that

The volume of a cone is equal to

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

Find the radius of the base of the cone

The circumference of a circle is equal to

[tex]C=2\pi r[/tex]

we have

[tex]C=56.52\ in[/tex]

substitute and solve for r

[tex]56.52=2(3.14)r[/tex]

[tex]r=56.52/6.28=9\ in[/tex]

Find the volume of the cone

[tex]V=\frac{1}{3}\pi r^{2}h[/tex]

we have

[tex]r=9\ in[/tex]

[tex]h=5\ in[/tex]

substitute

[tex]V=\frac{1}{3}(3.14)(9^{2})(5)=423.9\ in^{3}[/tex]

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