Exercise 25 Page 78

Practice makes perfect

a Using the following diagram as a reference point, we want to find the total area taken up by the bottom of the cans.

We have been told that the area of each can bottom is 9πcm^2. The total area is going to be the number of cans multiplied by the area of each can. This means that we need to multiply the given area by 6. A=6 * 9πcm^2 ⇒ A ≈ 113.04cm^2

b Now, using the same diagram, we want to know if the cans would fit into a box with a length of 16cm and a width of 12cm. To do so, we will first find the radius of one can. We know that the area of each can is 9πcm^2, so we can use the formula for area of a circle to find the radius.

A=π r^2 Let's substitute the area in and solve for the radius.

A=π r^2

Substitute

A= 9π

9π=π r^2

DivEqn

.LHS /π.=.RHS /π.

9=r^2

SqrtEqn

sqrt(LHS)=sqrt(RHS)

3=r

RearrangeEqn

Rearrange equation

r=3

Now that we know the radius of the circle, let's look to see what length and width is needed for the six cans.

There are 4 radii that create the width and 6 radii that create the length. We can use this to find the necessary dimensions of the box. Length:& 6 * 3 = 18cm Height:& 4 * 3 = 12cm The cans will not fit into the box because the length, 16cm, is less than than the space taken up by the cans.

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Exercises p.76-78

Exercise 25 Page 78

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