Exercise 13 Page 844

Use the formula for the volume of a pyramid.

233.8 cm^3

Practice makes perfect

The volume of a pyramid can be calculated using a known formula. In this formula B is the area of the base, and h is the height of a pyramid. V=1/3Bh In our exercise the base is a hexagon. Note that a hexagon can be divided into six congruent equilateral triangles.

Let's take one of the triangles. Since the height in the equilateral triangle divides it into two 30^(∘)-60^(∘)-90^(∘) triangles the height will be sqrt(3)2 times the side length.

Now we can calculate the area of a triangle using the formula.

A=1/2ah

SubstituteValues

Substitute values

A=1/2( 6)( 6sqrt(3)/2)

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Simplify right-hand side

MoveRightFacToNumOne

1/b* a = a/b

A=6/2(6sqrt(3)/2)

MultFrac

Multiply fractions

A=6*6sqrt(3)/2*2

Multiply

A=36sqrt(3)/4

ReduceFrac

a/b=.a /4./.b /4.

A=9sqrt(3)

The area of one triangle is 9sqrt(3) square centimeters. Now we can calculate the area of the hexagon. Since we divided it for six congruent triangles, we can multiply the area of one triangle by 6. B=6* 9sqrt(3) ⇕ B=54sqrt(3) We found that the area of the base is 54sqrt(3) cm^2. We are also given that the height is 7.5cm. Let's substitute these values into the formula and calculate V.

V=1/3Bh

SubstituteII

B= 54sqrt(3), h= 7.5

V=1/3( 54sqrt(3))( 7.5)

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Simplify right-hand side

Multiply

V=405sqrt(3)/3

CalcQuot

Calculate quotient

V=135sqrt(3)

UseCalc