Exercise 27 Page 603

We are given a cone.

To find the height, we can use the formula for the volume of a cone.

V = \frac{1}{3} π r^{2} h

Here,

r

is the radius and

h

is the height of the cone. We are given that the radius of the cone is

2.5

yards. The volume is

19.625

cubic yards. Let's substitute these values into the formula and solve for the height

h .

V = \frac{1}{3} π r^{2} h

$V = 19.625$ , $r = 2.5$

19.625 = \frac{1}{3} π (2.5)^{2} h

▼

Solve for

h

Calculate power

19.625 = \frac{1}{3} π (6.25) h

Commutative Property of Multiplication

19.625 = \frac{1}{3} (6.25) π h

$LHS \cdot 3 = RHS \cdot 3$

58.875 = 6.25 π h

$LHS / 6.25 = RHS / 6.25$

9.42 = π h

$LHS / π = RHS / π$

\frac{9 . 4 2}{π} = h

Rearrange equation

h = \frac{9 . 4 2}{π}

Use a calculator

h = 2.998479 \dots

Round to $1$ decimal place(s)

h \approx 3.0

We found out that the height of the cone is approximately

3.0

yards.