Exercise 12 Page 602

We want to find Carmen's mistake and correct it. To do so, we will calculate the volume of rice that will fill a cone-shaped 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 diameter 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 volume of a cone with the radius

r

and height

h

can be calculated by the following formula.

V = \frac{1}{3} π r^{2} h

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!

r = \frac{d}{2}

Substitute

$d = 4$

r = \frac{4}{2}

CalcQuot

Calculate quotient

r = 2

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 = \frac{1}{3} π r^{2} h

SubstituteII

$r = 2$ , $h = 6$

V = \frac{1}{3} π (2)^{2} (6)

PowToProdTwoFac

$a^{2} = a \cdot a$

V = \frac{1}{3} π \cdot 2 \cdot 2 \cdot 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.