Exercise 33 Page 604

We are given a pyramid. Its base is a square with a side of $6$ centimeters. Its height is $7.5$ centimeters.

The volume of a pyramid can also be calculated using a known formula.

V = \frac{1}{3} B h

Here

V

is the volume,

B

is the area of the base, and

h

is the height. The area of the rectangle equals to the square of the length its side.

B = a^{2}

Here

a

is

6 .

We already have enough information to calculate the volume of the cone.

V = \frac{1}{3} B h

Rewrite $B$ as $a^{2}$

V = \frac{1}{3} a^{2} h

$a = 6$ , $h = 7.5$

V = \frac{1}{3} (6)^{2} (7.5)

▼

Evaluate right-hand side

Calculate power

V = \frac{1}{3} (36) (7.5)

V = \frac{1}{3} (270)

$\frac{a}{c} \cdot b = \frac{a \cdot b}{c}$

V = \frac{2 7 0}{3}

Calculate quotient

V = 90

The volume of the pyramid is

90

cubic centimeters.