Learn Mode

Ratios and Scaling of Geometric Figures Quiz

Go to Quiz Page

Which of the following is a ratio?

2:3

Explanation

Ratio expresses a relationship between two quantities.

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.

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.

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.

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. 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.

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.

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.

12. The scale factor between two similar cylinders is 1:2. If the radius of the smaller cylinder is 3 cm, what is the radius of the larger cylinder?

6 cm

Explanation

Scale factor applies to all corresponding dimensions.

#10

13. In a similar set of rectangles, the ratio of the lengths is 3:4. If the area of the larger rectangle is 96 square units, what is the area of the smaller rectangle?

36 square units

Explanation

Area is proportional to the square of the length ratio.

#11

16. The sides of a triangle are in the ratio 5:12:13. What is the measure of the largest angle in the triangle?

90 degrees

Explanation

The largest angle is opposite the longest side in a triangle.

#12

18. The perimeter of a rectangle is 30 cm, and its length is in the ratio 2:3. What is the width of the rectangle?

8 cm

Explanation

Find the length and then calculate the width using the perimeter formula.

#13

22. The lengths of two sides of a rectangle are in the ratio 3:5. If the area is 120 square units, what is the length of the shorter side?

6 units

Explanation

Use area formula to find one side length, then find the other.

#14

23. The perimeter of a triangle is 24 cm. If the sides are in the ratio 3:4:5, what is the length of the longest side?

15 cm

Explanation

Longest side is found by multiplying the ratio with the total perimeter.

#15

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.

#16

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.

#17

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.

#18

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.

#19

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.

#20

15. If the ratio of the areas of two similar circles is 4:9, what is the ratio of their radii?

2:3

Explanation

Area ratio is the square of the radius ratio.

#21

17. The scale factor between two similar cones is 1:3. If the volume of the smaller cone is 27 cubic units, what is the volume of the larger cone?

81 cubic units

Explanation

Volume ratio is the cube of the scale factor.

#22

19. The areas of two similar triangles are in the ratio 16:25. If the length of a side of the smaller triangle is 8 cm, what is the length of the corresponding side of the larger triangle?

15 cm

Explanation

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

#23

21. The surface areas of two similar cylinders are in the ratio 1:4. If the radius of the smaller cylinder is 2 cm, what is the radius of the larger cylinder?

6 cm

Explanation

Surface area ratio is the square of the radius ratio.

#24

24. In a similar set of squares, the ratio of the lengths is 2:3. If the area of the smaller square is 36 square units, what is the area of the larger square?

81 square units

Explanation

Area is proportional to the square of the length ratio.

#25

25. The scale factor between two similar triangles is 3:7. If the area of the larger triangle is 147 square units, what is the area of the smaller triangle?

63 square units

Explanation

Area ratio is the square of the scale factor.

Ratios and Scaling of Geometric Figures Quiz

Which of the following is a ratio?

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

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

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

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

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

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?

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. The scale factor between two similar cylinders is 1:2. If the radius of the smaller cylinder is 3 cm, what is the radius of the larger cylinder?

13. In a similar set of rectangles, the ratio of the lengths is 3:4. If the area of the larger rectangle is 96 square units, what is the area of the smaller rectangle?

16. The sides of a triangle are in the ratio 5:12:13. What is the measure of the largest angle in the triangle?

18. The perimeter of a rectangle is 30 cm, and its length is in the ratio 2:3. What is the width of the rectangle?

22. The lengths of two sides of a rectangle are in the ratio 3:5. If the area is 120 square units, what is the length of the shorter side?

23. The perimeter of a triangle is 24 cm. If the sides are in the ratio 3:4:5, what is the length of the longest side?

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

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?

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?

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?

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

15. If the ratio of the areas of two similar circles is 4:9, what is the ratio of their radii?

17. The scale factor between two similar cones is 1:3. If the volume of the smaller cone is 27 cubic units, what is the volume of the larger cone?

19. The areas of two similar triangles are in the ratio 16:25. If the length of a side of the smaller triangle is 8 cm, what is the length of the corresponding side of the larger triangle?

21. The surface areas of two similar cylinders are in the ratio 1:4. If the radius of the smaller cylinder is 2 cm, what is the radius of the larger cylinder?

24. In a similar set of squares, the ratio of the lengths is 2:3. If the area of the smaller square is 36 square units, what is the area of the larger square?

25. The scale factor between two similar triangles is 3:7. If the area of the larger triangle is 147 square units, what is the area of the smaller triangle?

Test Your Knowledge