Question

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

Answer 1

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

Answer 2

Option D
`423.9\ in^(3)`

Explanation:

we know that

The volume of a cone is equal to

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

Find the radius of the base of the cone

The circumference of a circle is equal to

`C=2\pi r`

we have

`C=56.52\ in`

substitute and solve for r

`56.52=2(3.14)r`

`r=56.52/6.28=9\ in`

Find the volume of the cone

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

we have

`r=9\ in`

`h=5\ in`

substitute

`V=(1)/(3)(3.14)(9^(2))(5)=423.9\ in^(3)`