Exercise 16 Page 844

Use the formula for the volume of a pyramid.

18 cm

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 Since in our exercise we are asked to find the height, let's solve the above formula for h using the inverse operations.

V=1/3Bh

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Solve for h

MoveRightFacToNumOne

1/b* a = a/b

V=Bh/3

MultEqn

LHS * 3=RHS* 3

3V=Bh

DivEqn

.LHS /B.=.RHS /B.

3V/B=h

RearrangeEqn

Rearrange equation

h=3V/B

As we are given the volume of our pyramid we need to find the base area. Let's use the fact that the base is a right triangle with a leg of 5 cm and the hypotenuse of 10cm.

Now we will calculate the length of the other leg using the Pythagorean Theorem.

x^2+ 8^2= 10^2

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Solve for x

CalcPow

Calculate power

x^2+64=100

SubEqn

LHS-64=RHS-64

x^2=36

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(36)

CalcRoot

Calculate root

x=6

Note that, when solving the above equation, we only needed to consider the principal root because x is a positive number. We found that the other leg is approximately 6. To calculate the base area let's use the formula for area of a triangle.

B=1/2ab

SubstituteValues

Substitute values

B=1/2( 8)( 6)

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Simplify right-hand side

Multiply

B=1/2*48

MoveRightFacToNumOne

1/b* a = a/b

B=48/2

CalcQuot