MathematicsRatio Analysis
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Ratios and Scaling of Geometric Figures Quiz

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#1

Which of the following is a ratio?

2:3
Explanation

Ratio expresses a relationship between two quantities.

#2

14. The perimeter of a square is 36 cm. What is the length of one side of the square?

6 cm
Explanation

Perimeter formula: Perimeter = 4 * side length.

#3

20. The circumference of a circle is 36 cm. What is the radius of the circle?

9 cm
Explanation

Circumference formula: Circumference = 2 * π * radius.

#4

If the scale factor of two similar figures is 3:4, what is the ratio of their areas?

9:16
Explanation

The ratio of areas is the square of the scale factor.

#5

In a rectangle, if the length is doubled and the width is halved, what is the effect on the ratio of length to width?

Remains the same
Explanation

The ratio of length to width is unaffected by scaling.

#6

6. The volumes of two similar cubes are in the ratio 8:27. What is the ratio of their side lengths?

2:3
Explanation

Volume ratio is the cube of the ratio of side lengths.

#7

8. A map of a city uses a scale of 1:10,000. If two points on the map are 5 cm apart, what is the actual distance between them in kilometers?

5 km
Explanation

Use scale to convert map distance to actual distance.

#8

10. If the ratio of the areas of two similar triangles is 9:16, and the length of a side of the smaller triangle is 6 cm, what is the length of the corresponding side of the larger triangle?

12 cm
Explanation

Area ratio is the square of the ratio of corresponding side lengths.

#9

The ratio of the angles in a triangle is 2:3:5. What is the measure of the smallest angle?

20 degrees
Explanation

The smallest angle is found by multiplying the smallest ratio by the total degrees in a triangle.

#10

If the perimeter of a square is doubled, what is the effect on the ratio of the areas of the original square and the new square?

Remains the same
Explanation

Area ratio is independent of changes in perimeter.

#11

7. The base of a rectangular prism is in the ratio 2:5, and its height is 8 cm. If the volume is 320 cubic centimeters, what is the length of the base?

10 cm
Explanation

Volume formula: Volume = Base Area * Height.

#12

9. The lengths of the diagonals of a rectangle are in the ratio 1:2. If the length of the shorter diagonal is 6 cm, what is the length of the longer diagonal?

10 cm
Explanation

Diagonal ratio is directly proportional to side length ratio.

#13

11. The angles of a triangle are in the ratio 2:3:5. What is the measure of the smallest angle?

20 degrees
Explanation

The smallest angle is found by multiplying the smallest ratio by the total degrees in a triangle.

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