Seeing Geometry in Everyday Life

Education · 10 questions

Everyday applications and calculations involving geometry.

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1. Assumptions: A rectangular table measures 1.2 m × 0.8 m. What is its surface area in m²?

   1. 0.96 m²
   2. 0.88 m²
   3. 0.72 m²
   4. 1.00 m²
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   A) 0.96 m²

2. Assumptions: A ladder’s base is 4 m from a wall, its contact point is 3 m above the ground, and the ground is level. How long is the ladder?

   1. 5 m
   2. 4.5 m
   3. 4 m
   4. 6 m
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   A) 5 m

3. Assumptions: A square tile has a side length of 30 cm. What is its diagonal length?

   1. 60 cm
   2. 30√2 cm
   3. 45 cm
   4. 30√3 cm
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   B) 30√2 cm

4. Assumptions: A clock shows 3:15. What is the smaller angle between its hour and minute hands?

   1. 30°
   2. 0°
   3. 15°
   4. 7.5°
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   D) 7.5°

5. Assumptions: A 2 m object casts a 3 m shadow. At the same time, a tree casts a 12 m shadow. How tall is the tree?

   1. 8 m
   2. 6 m
   3. 4 m
   4. 10 m
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   A) 8 m

6. Assumptions: A bicycle wheel has a diameter of 0.7 m. How far does it travel in one revolution?

   1. π m
   2. 0.35π m
   3. 1.4π m
   4. 0.7π m
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   D) 0.7π m

7. Assumptions: A regular hexagon has side length 10 cm. What is its area in cm²? (A = (3√3/2)·a²)

   1. 300√3 cm²
   2. 100√3 cm²
   3. 150√3 cm²
   4. 75√3 cm²
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   C) 150√3 cm²

8. Assumptions: Each 1 m × 1 m square tile is divided into two congruent right-triangle pieces. How many pieces cover a 6 m² floor?

   1. 6
   2. 12
   3. 8
   4. 24
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   B) 12

9. Assumptions: A cylindrical water tank has radius 0.5 m and height 2 m. What is its volume in m³? (V = πr²h)

   1. π m³
   2. 1.0π m³
   3. 0.5π m³
   4. 0.25π m³
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   C) 0.5π m³

10. Which geometric concept finds the shortest path between two points on the same side of a line that must touch the line?

    1. Rotation
    2. Reflection
    3. Translation
    4. Dilation
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    B) Reflection