The base of a 6-inch long ice cream cone with a diameter of 2 inches, is cut 0.25 inches from the base. This cut creates two shapes, one is a cone, and the other one resembles a cylinder since it was cut so close to the base. What is the BEST estimate for the volume of the shape that resembles a cylinder?
A)0.26 cubic inches
B)0.52 cubic inches
C)0.79 cubic inches
D)2.66 cubic inches
Is it B?
pi is about 22/7
.25 * pi r^2 =22/(7 *4) = 22/28 = .79
To find the volume of the shape that resembles a cylinder, we need to find the height and radius of the cylinder.
Given:
- The ice cream cone is 6 inches long
- The diameter of the ice cream cone is 2 inches
- The cut is made 0.25 inches from the base
To find the height of the cylinder:
Since the cut is made 0.25 inches from the base, the height of the cylinder is 6 inches - 0.25 inches = 5.75 inches.
To find the radius of the cylinder:
The diameter of the ice cream cone is 2 inches, so the radius is half of that, which is 2/2 = 1 inch.
Now that we have the height and radius, we can calculate the volume of the cylinder using the formula: volume = π * r^2 * h.
Volume = π * (1 inch)^2 * 5.75 inches
Using the value of π ≈ 3.14, and simplifying the equation, we get:
Volume ≈ 3.14 * 1 inch * 1 inch * 5.75 inches
Volume ≈ 3.14 * 5.75 cubic inches
Volume ≈ 18.095 cubic inches
The BEST estimate for the volume of the shape that resembles a cylinder is approximately 18.095 cubic inches.
Therefore, the correct answer is not B) 0.52 cubic inches.
To find the best estimate for the volume of the shape that resembles a cylinder, we first need to determine the radius of the base of the cylinder.
Given that the diameter of the base is 2 inches, the radius will be half of that, which is 1 inch.
Next, we need to determine the height of the cylinder. Since the cut is made 0.25 inches from the base of the cone, the height of the cylinder is 6 inches - 0.25 inches = 5.75 inches.
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Now, let's plug in the values and calculate the volume:
V = π(1 inch)^2 * 5.75 inches
V ≈ 3.14 * 1 inch * 1 inch * 5.75 inches ≈ 17.25 cubic inches
So, the best estimate for the volume of the shape that resembles a cylinder is 17.25 cubic inches.
Therefore, the correct answer is not option B.