MathematicsProportionality
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Mathematical Scaling and Proportional Relationships Quiz

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#1

Which of the following is an example of direct variation?

y = 4x
Explanation

Direct variation means as one variable increases, the other increases proportionally.

#2

If y is inversely proportional to x and y = 12 when x = 4, what is the value of y when x = 8?

18
Explanation

In inverse proportionality, as one variable increases, the other decreases proportionally.

#3

If a rectangle has sides in the ratio 3:4, and the perimeter is 28 units, what is the length of the longer side?

12
Explanation

The longer side in the ratio corresponds to 4x where x is a common factor.

#4

If the scale factor of two similar triangles is 1:3, and the area of the smaller triangle is 12 square units, what is the area of the larger triangle?

27
Explanation

Area scales with the square of the scale factor in similar figures.

#5

If the length of a rectangle is doubled, and the width is tripled, how does the area of the rectangle change?

It becomes four times the original
Explanation

Area is multiplied by the scaling factor of both dimensions.

#6

In a right-angled triangle, if the lengths of the legs are 5 units and 12 units, what is the length of the hypotenuse?

13
Explanation

Use Pythagoras' theorem: c^2 = a^2 + b^2.

#7

If the scale factor between two similar rectangles is 1:2, and the area of the smaller rectangle is 36 square units, what is the area of the larger rectangle?

72
Explanation

Area scales with the square of the scale factor in similar figures.

#8

The volume of a cube is 125 cubic units. What is the length of each side?

5
Explanation

Volume of a cube is side^3.

#9

If the price of 3 books is $24, what is the cost of 6 books if the prices are in direct proportion?

$36
Explanation

Direct proportionality means the price scales linearly with quantity.

#10

The speed of a car is directly proportional to the distance it travels. If a car travels 120 miles in 2 hours, how far will it travel in 5 hours?

300 miles
Explanation

Direct proportionality means constant speed.

#11

If the base of a rectangle is increased by 20% and the height is decreased by 10%, how does the area of the rectangle change?

It increases by 10%
Explanation

Area change is influenced by both dimensions.

#12

If a cylindrical tank has a radius of 4 meters and a height of 6 meters, what is its volume?

64π cubic meters
Explanation

Volume of a cylinder: V = πr^2h.

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