Exercise 10 Page 436

We want to determine how many cupcakes we can decorate with 2 bags of icing. We know that the icing is put into cone-shaped pastry bags with a height of 1 foot and a diameter of 3.5 inches. Let's start by finding the volume of icing in one pastry bag.

We need to convert the measurements to the same unit. Let's convert the height into inches. 1 ft * 12in/1 ft = 12 inNext, we divide the diameter by 2 to get the radius. d/2=r ⇒ 3.5in/2= 1.75in We will substitute 12 for h and 1.75 for r into the formula for the volume of a cone to get the volume of icing in the pastry bag.

V=1/3π r^2 h

SubstituteII

h= 12, r= 1.75

V=1/3π ( 1.75)^2 12

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Solve for V

CalcPow

Calculate power

V=1/3π (3.0625) 12

Multiply

Multiply

V=1/3π (35.75)

MoveRightFacToNumOne

1/b* a = a/b

V=π (35.75)/3

UseCalc

Use a calculator

V=37.437312 ...

RoundDec

Round to 1 decimal place(s)

V≈ 37.4

A pastry bag contains about 37.4 cubic inches of icing. We know that we use about 1.35 cubic inches of icing per cupcake. If we divide the total amount of icing by the amount we need per cupcake we get the amount of cupcakes we can decorate with one pastry bag. 37.4in^2icing/1.35in^2icing per cupcake ≈ 28 cupcakes We can decorate about 28 cupcakes with one pastry bag. Finally, we want to know how many cupcakes we can decorate with 2 bags, so we will multiply this amount by 2. 28 * 2 = 56 cupcakes We can decorate about 56 cupcakes with 2 pastry bags.