The side length of a square was increased by a factor of 3. The new, enlarged area of the square is 1 over 9 times as large as the original area of the square.
Select one:
True
False
True
The dimensions of a can of sparking water were increased by a factor of 1.2. The new, enlarged volume of the can is 1.728 times as large as the original volume of the can.
Select one:
True
False
False
The length, width and height of a crate were decreased by a factor of 3 over 5. The scale factor relating the volume of the reduced crate to the original crate can be written in the form a over b, where
a = Answer
b = Answer
a = 3/5
b = 1
Martha is conducting a science experiment where she inflates a balloon using the gasses created in a chemical reaction. Martha is recording the balloon's circumference over time to see how the volume of gas inside the balloon changes. Martha's first measurement of the circumference is 22 cm. Her last measurement of the circumference is 43 cm.
What is the scale factor relating the volume of the balloon at the end of her experiment compared to the volume of the balloon at her first measurement.
Select one:
a.
Volume Scale Factor = 1.95
b.
Volume Scale Factor = 7.47
c.
Volume Scale Factor = 0.13
d.
There is not enough information to find the Volume Scale Factor.
d. There is not enough information to find the Volume Scale Factor.
The relationship between circumference and volume is not linear, so measurements of circumference alone cannot be used to determine the scale factor for volume.
The final volume of a balloon once it is fully inflated is 512 times larger than the volume it held originally. The scale factor relating the diameter of the fully inflated balloon to the original balloon is 8.
Select one:
True
False
True
A factory is producing key-chains with a coffee cup on them. The surface area of the sleeve that wraps around the actual coffee cup is 183 cm2. The surface area of the sleeve that wraps around the key-chain cup is 7.32 cm2.
The Area Scale Factor that represents the reduction of the actual coffee cup sleeve to the one on the key-chain is Answer
(recorded as a decimal, include the leading 0 if there is one, example: .5 x 0.5Check mark).
The Linear Scale Factor that represents the reduction of the actual coffee cup sleeve to the one on the key-chain is Answer
(recorded as a decimal, include the leading 0 if there is one, example: .5 x 0.5Check mark).
The Area Scale Factor is 0.04.
The Linear Scale Factor is 0.2.
A circle has an area of 45 cm2. The radius of that circle is reduced by a factor of 2 over 5. Complete the set up of the proportion below to find the reduced area.
L e t space x space equals space t h e space r e d u c e d space a r e a
a over 45 equals b over c
a = blank
b = blank
c = blank
When you solve the proportion for x, you will find the reduced area of the circle. The reduced area of the circle is blank .
x 4 25 2 5 8 125 7.2 18 2.88
a = x
b = 45
c = (2/5)^2 = 4/25
Solving the proportion:
a/45 = b/(4/25)
Cross-multiplying:
a * (4/25) = 45 * b
4a/25 = 45b
Simplifying:
4a = 25 * 45b
4a = 1125b
Dividing by 4:
a = (1125/4)b
So, a = (1125/4)b and c = 4/25.
The reduced area of the circle is given by x.
The area of the base of a soup can is 44.2 cm2. The height of that soup can is 11 cm. The soup company is producing an enlarged can for a store display. The enlarged can is 12 times as tall as the original soup can. What is the volume of the enlarged soup can?
The Linear Scale Factor as a whole number is Answer
.
The Volume Scale Factor as a whole number is Answer
.
You can create a proportion to solve for the enlarged volume in the form V o l u m e space S c a l e space F a c t o r equals fraction numerator s c a l e d space v o l u m e over denominator o r i g i n a l space v o l u m e end fraction.
*Note that you can write any whole number as a fraction by putting over 1. For example, the whole number 5 written as a fraction is 5 over 1.
Below is a proportion that can be used to find the enlarged volume of the soup can. Complete the set up of this proportion.
L e t space x space equals space t h e space e n l a r g e d space v o l u m e space o f space t h e space s o u p space c a n
a over 1 equals b over c
a = Answer
b = Answer
c = Answer
Were you given the original volume of the soup can? Could you use the information given to find the original volume of the soup can?
The volume of the enlarged soup can (to the nearest cm3) is Answer
cm3.
(Record your answer with no commas or spaces: 10000 Check mark 10,000 x 10 000 x)
The Linear Scale Factor as a whole number is 12.
The Volume Scale Factor as a whole number is 12^3 = 1728.
Setting up the proportion:
Let x be the enlarged volume of the soup can.
a/1 = b/c
a = x
b = 1728
c = 1
We were not given the original volume of the soup can. Without that information, we cannot directly find the original volume.
To find the enlarged volume of the soup can, we can use the formula for the volume of a cylinder:
Volume = π * r^2 * h
Given:
Area of the base = 44.2 cm^2
Height = 11 cm
Linear Scale Factor = 12
The radius of the enlarged can is 12 times the radius of the original can. Since the area scales with the square of the scale factor, the area of the enlarged base is (12^2) * 44.2 = 6338.4 cm^2.
Now, we can calculate the volume of the enlarged soup can:
Volume = π * (radius^2) * height
= π * (6338.4 / π) * (11 * 12)
= 6338.4 * 132
≈ 837091.2 cm³
The volume of the enlarged soup can (to the nearest cm³) is 837091 cm³.
The volume of a volleyball when fully inflated is 321.54 in3. The volume of a soccer ball with fully inflated is 371.43 in3. What is the scale factor relating the area of this enlargement?
The Volume Scale Factor representing this enlargement can be written in the form V S F equals a over b where,
a = blank
b = blank
Remember that V S F space equals space k cubed, where k = the Linear Scale Factor.
This means that k equals c-th root of a over b end root, where
a = blank
b = blank
c = blank
The Linear Scale Factor for this enlargement is k = blank (rounded to the nearest hundredth).
The scale factor relating the area of this enlargement is blank (rounded to the nearest hundredth).
3 371.43 321.54 1.05 1.10 2 1.16 1.34 0.87 0.95 0.91
The Volume Scale Factor can be written as a/b, where:
a = 321.54
b = 371.43
The Linear Scale Factor, k, can be found by taking the cube root of a/b:
k = (a/b)^(1/3)
Substituting the values:
k = (321.54/371.43)^(1/3)
Calculating k:
k ≈ 0.920
The scale factor relating the area of this enlargement is equal to the square of the Linear Scale Factor, which is k^2:
Scale factor = k^2 ≈ 0.920^2 ≈ 0.846
So, the scale factor relating the area of this enlargement is approximately 0.846.
A factory produces a set of 4 nesting, plastic storage bins. The volume of the smallest bin is 2000 cm3. The volume of the largest bin is 0.054 m3. What is the linear scale factor that represents this enlargement?
Select one:
a.
37 037
b.
27
c.
9
d.
3
To find the linear scale factor, we need to convert the volumes of the bins to the same unit of measurement.
Volume of the smallest bin = 2000 cm³ (cubic centimeters)
Volume of the largest bin = 0.054 m³ (cubic meters)
To convert cm³ to m³, we divide by 1000000 (since 1 m³ = 1,000,000 cm³):
2000 cm³ = 2000/1000000 m³ = 0.002 m³
Now, we can find the linear scale factor:
Linear scale factor = (volume of largest bin) / (volume of smallest bin)
= 0.054 m³ / 0.002 m³
= 27
Therefore, the linear scale factor that represents this enlargement is 27.
(Note: The options in the answer choices seem to be incorrectly formatted. The correct linear scale factor is 27, which is not exactly equal to any of the given answer choices.)