We want to find Carmen's mistake and correct it. To do so, we will calculate the of rice that will fill a decorative vase. Let's start by drawing the vase. We know that the vase is a cone with the height of 6 inches and the of 4 inches.
To find the volume of rice that will fill the vase, we need to find the volume of the vase. Recall that the with the
r and height
h can be calculated by the following formula.
V=31πr2h
In this case, we are given the diameter and the height of the cone. To find the radius of the cone, we need to divide the diameter
d by
2. Let's do it!
We got that the radius is equal to
2 inches. Therefore, we can substitute the height and the radius into the formula and calculate the volume of the cone.
V=31πr2h
V=31π(2)2(6)
V=31π⋅2⋅2⋅6
Now let's take a closer look at Carmen's solution.
We can see that Carmen used the formula incorrectly. Probably, she substituted the diameter of the cone instead of the radius of the cone in the formula. Let's circle her mistake.
Next, we will continue calculating the volume correctly.
V=31π⋅2⋅2⋅6
V=31⋅24⋅π
V=324π
V=25.132…
V≈25.1
Finally, we got that the volume of the vase is equal to about
25.1 cubic inches. This means that the volume of rice that will fill the vase is also about
25.1 cubic inches.