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R5 Reading Assignment - Scale Factor*
Opracowany przez: Cason
 
 

3:2

2:3

The ratio of the lengths of corresponding sides in

similar figures (same shape but different size) is

called scale factor.  It may be expressed as a

fraction, decimal, percent, or whole number.  It

may be large number first or small number first.  

What would NOT be a scale factor for the shapes

below?

         3 cm                 2 cm

.6666667

2:1

6 cm by 10 cm

2 cm by 3 cm

Since a scale factor may be large-to-small or small-to-

large and in fraction, percent, or decimal form, all

answers were right except for 2:1.  

Neither 3:2 or 2:3 will simplify to 2:1.

 

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle has a scale factor of 1:2 or 50%.  Find its

length and width.

1.5 cm by 2.5 cm

2 cm by  2.5 cm

6 cm by 10 cm

2 cm by 3 cm

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle has a scale factor of 1:2 or 50%.  Find its

length and width.  Since 50% equals 0.5 and 1/2,

multiply both numbers separately by 0.5 or 1/2.  We

can divide by the reciprocal 2 also.  The answer is

1.5 cm. by 2.5 cm.

 

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle has a scale factor of 200%.  Find its

dimensions.

2 cm by  2.5 cm

1.5 cm by 2.5 cm

80 cm

A rectangle has sides of 3 cm and 5 cm.  A similar

rectangle has a scale factor of 200%.  Find its

dimensions.  200% equals 2, so multiply the

perimeter by 2.  The answer is 6 cm by 10 cm.

 

If we know one shape's perimeter, that both are

similar, and the scale factor, we can solve for the

other shape's perimeter by multiplying each number

by the scale factor.   If the first shape has a perimeter 

of 16 cm. and the scale factor is 50%, the second

shape's perimeter is...

32 cm

8 cm

80 cm

32 cm

3200 cm

The first shape has a perimeter of 16 cm. and the

scale factor is 50%, so multiply 16 by 0.5, 1/2, or

divide by the reciprocal of 2.  The answer is 8 cm.

 

If the perimeter is 16 cm. and the scale factor 200%,

the perimeter of the similar shape is...

8 cm

80 cm

45 square centimeters

90 square centimeters

The perimeter of the first shape is 16 cm. and the

scale factor 200% (which equals 2).   The perimeter of

the similar shape is 32.  Multiply 16 by 2.

 

Because area is in square units, we have to square

the scale factor before multiplying it by the area of

the first shape.  Our original shape was 3 cm. by 5 cm. 

Therefore its area is 3 x 5 or 15 square centimeters. 

A similar shape with a scale factor of 3 would have an

area of...

135 square centimeters

32 square centimeters

9.6 square centimeters

24 square centimeters

Because area is in square units, we have to square the

scale factor before multiplying it by the area of the

first shape.  Our original shape was 3 cm. by 5 cm. 

Therefore its area is 3 x 5 or 15 square centimeters. 

A similar shape with a scale factor of 3 would have an

area of...Square the scale factor 3.  It becomes 3 x 3

or 9.  Then multiply 9 times 15.  The answer is 135

square centimeters.

 

If the original area was 60 square centimeters and

the scale factor 40%, the new shape's area would be...

96 square centimeters

2.4 square centimeters

60 x 2 x 2 x 2

60 x 3 x 3 x 3

If the original area was 60 square centimeters and

the scale factor 40%, the new shape's area would be...

60 x .4 x .4 = 9.6.

 

Because volume is in cubic units, we have to cube (to

the 3rd power) the scale factor to convert volume of

similar 3-dimension shapes.  If the first has a volume

of 60 cubic units and the scale factor is 2, the volume

of the second shape would be 60 x 2 x 2 x 2.  What if

the first shape has a volume of 60 cubic units and the

scale factor is 3...

60 x 2 x 2

60 x 3 x 3

60 x 1/4 x 1/4 x 1/4

60 x .25 x .25

Because volume is in cubic units, we have to cube (to

the 3rd power) the scale factor to convert volume of

similar 3-dimension shapes.  If the first has a volume

of 60 cubic units and the scale factor is 2, the volume

of the second shape would be 60 x 2 x 2 x 2.  What if

the first shape has a volume of 60 cubic units and the

scale factor is 3...60 x 3 x 3 x 3.

 

The volume of the first shape is 60 cubic units and

the scale factor is 25%...

60 x .25

60 ÷ 0.25

2 cm. by 5 cm.

20 cm. 50 cm.

The volume of the first shape is 60 cubic units and the

scale factor is 25%...Volume is in cubic units so we

cube the scale factor.  25% equals the fraction 1/4. 

Multiply 1/4 or 0.25 by itself three times and then

times the first shape's area.

 

If the first shape is 4 cm.  by  10 cm and the scale

factor is 3, what are the new shape's dimensions?

90 cm. by 36 cm.

12 cm. by 30 cm.

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