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McGraw Hill Integrated II, 2012
MH
McGraw Hill Integrated II, 2012 View details
5. Volumes of Pyramids and Cones
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Exercise 41 Page 847

Use the formula for the volume of a cone.

A

Practice makes perfect

A conical sand toy can be modeled by the following cone.

We are asked how many cubic centimeters of sand it will hold when it is filled to the top. This tells us that we should find the volume of the cone. First, let's find the radius of the base r. We will use the Pythagorean Theorem for the right triangle.

r^2+4^2=5^2
â–¼
Solve for r
CalcPow

Calculate power

r^2+16=25
SubEqn

LHS-16=RHS-16

r^2=9
SqrtEqn

sqrt(LHS)=sqrt(RHS)

sqrt(r^2)=sqrt(9)
SqrtPowToNumber

sqrt(a^2)=a

r=sqrt(9)
CalcQuot

Calculate quotient

r=3

Therefore, the radius of the base is r=3 centimeters. Now, let's use the formula for the volume of a cone.

V=1/3Ï€ r^2h
â–¼
Substitute values and evaluate
SubstituteII

r= 3, h= 4

V=1/3Ï€ ( 3)^2( 4)
CalcPowProd

Calculate power and product

V=1/3* 36Ï€
MoveRightFacToNumOne

1/b* a = a/b

V=36Ï€/3
CalcQuot

Calculate quotient

V=12Ï€

This tells us that the canonical sand toy can hold 12Ï€ cubic centimeters of sand. This corresponds to option A.

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