The volume of a cone is 54 pi cubic inches. The radius and height of the cone are both reduced by a factor of 3 to create a new cone. What is the volume of the new cone?
Is the volume of the new cone 18pi cu in
A. 2 pi cu inches
B. 6 pi cu inches
C. 9 pi cu inches
D. 18 pi cu inches
Is the answer 18 pi cu inches
V = (pi*r^2*h) / 3 = 54pi.
Vn = (pi*(r/3)^2*(h/3)) / 3 = 54pi,
Vn = (pi*(r^2/9)*(h/3)) / 3 = 54pi,
Vn = (pi*r^2*(1/27)*h) / 3 = 54pi,
We have divided the left side of our Eq by 27. Therefore , we must divide
the rt. side by 27 also:
Vn = (pi*r^2*(1/27)*h) / 3 = 2pi. =
New volume = "A".
To find the volume of the new cone, we need to calculate the new radius and height of the cone, and then use the volume formula for a cone.
Let's start with the given information:
Volume of the original cone = 54 pi cubic inches
We know that the volume of a cone is given by the formula:
V = (1/3) * pi * r^2 * h
where V is the volume, r is the radius, and h is the height of the cone.
Since both the radius and height of the original cone are reduced by a factor of 3, the new radius (r1) and new height (h1) are:
r1 = (1/3) * r
h1 = (1/3) * h
Substituting these values into the volume formula for the new cone, we get:
V1 = (1/3) * pi * (r1)^2 * h1
Simplifying:
V1 = (1/3) * pi * ((1/3) * r)^2 * ((1/3) * h)
V1 = (1/3) * pi * (1/9) * r^2 * h
V1 = (1/27) * pi * r^2 * h
Now we can find the volume of the new cone by multiplying the volume of the original cone by (1/27):
V1 = (1/27) * (54 pi)
V1 = 2 pi
So, the volume of the new cone is 2 pi cubic inches.
Therefore, the correct answer is A. 2 pi cubic inches.