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McGraw Hill Integrated II, 2012 View details

5. Volumes of Pyramids and Cones

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Exercise 15 Page 844

Use the formula for the volume of a pyramid.

35.6 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 we are given that the base is a right triangle with a leg 5 cm and hypotenuse 10.2 cm. Let's draw a diagram of this base.

Notice that we can find the length of the other leg using the Pythagorean Theorem.

x^2+ 5^2= 10.2^2

▼

Solve for x

CalcPow

Calculate power

x^2+25=104.04

SubEqn

LHS-25=RHS-25

x^2=79.04

SqrtEqn

sqrt(LHS)=sqrt(RHS)

x=sqrt(79.04)

CalcRoot

Calculate root

x=8.8904...

RoundDec

Round to 1 decimal place(s)

x≈ 8.9

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 has a length of approximately 8.9. Let's use this information to calculate the base area which will be the area of a triangle.

B=1/2ab

SubstituteValues

Substitute values

B=1/2( 5)( 8.9)

▼

Simplify right-hand side

Multiply

B=1/2*44.5

MoveRightFacToNumOne

1/b* a = a/b

B=44.5/2

CalcQuot