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Arrange the following three-dimensional objects in the descending order of their volumes:
(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm
(ii) A cube of side 8 cm
(iii) A cylinder with base radius 7 cm and height 7 cm
(iv) A sphere of radius 7 cm
  • a)
    (i), (ii), (iii), (iv)
  • b)
    (ii), (i), (iv), (iii)
  • c)
    (iii), (ii), (i), (iv)
  • d)
    (iv), (iii), (ii), (i)
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Arrange the following three-dimensional objects in the descending orde...
Volume Calculations
To arrange the objects in descending order of their volumes, we first need to calculate the volume of each object.
1. Volume of the Cuboid
- Formula: Volume = Length × Width × Height
- Calculation:
Volume = 10 cm × 8 cm × 6 cm = 480 cm³
2. Volume of the Cube
- Formula: Volume = Side³
- Calculation:
Volume = 8 cm × 8 cm × 8 cm = 512 cm³
3. Volume of the Cylinder
- Formula: Volume = π × Radius² × Height
- Calculation:
Volume = π × (7 cm)² × 7 cm
Volume ≈ 3.14 × 49 cm² × 7 cm ≈ 1077.58 cm³
4. Volume of the Sphere
- Formula: Volume = (4/3) × π × Radius³
- Calculation:
Volume = (4/3) × π × (7 cm)³
Volume ≈ (4/3) × 3.14 × 343 cm³ ≈ 1436.76 cm³
Final Volume Comparison
- Cuboid: 480 cm³
- Cube: 512 cm³
- Cylinder: 1077.58 cm³
- Sphere: 1436.76 cm³
Descending Order of Volumes
- Sphere (1436.76 cm³)
- Cylinder (1077.58 cm³)
- Cube (512 cm³)
- Cuboid (480 cm³)
Thus, the correct order is D: (iv), (iii), (ii), (i).
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Arrange the following three-dimensional objects in the descending order of their volumes:(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm(ii) A cube of side 8 cm(iii) A cylinder with base radius 7 cm and height 7 cm(iv) A sphere of radius 7 cma)(i), (ii), (iii), (iv)b)(ii), (i), (iv), (iii)c)(iii), (ii), (i), (iv)d)(iv), (iii), (ii), (i)Correct answer is option 'D'. Can you explain this answer?
Question Description
Arrange the following three-dimensional objects in the descending order of their volumes:(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm(ii) A cube of side 8 cm(iii) A cylinder with base radius 7 cm and height 7 cm(iv) A sphere of radius 7 cma)(i), (ii), (iii), (iv)b)(ii), (i), (iv), (iii)c)(iii), (ii), (i), (iv)d)(iv), (iii), (ii), (i)Correct answer is option 'D'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Arrange the following three-dimensional objects in the descending order of their volumes:(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm(ii) A cube of side 8 cm(iii) A cylinder with base radius 7 cm and height 7 cm(iv) A sphere of radius 7 cma)(i), (ii), (iii), (iv)b)(ii), (i), (iv), (iii)c)(iii), (ii), (i), (iv)d)(iv), (iii), (ii), (i)Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Arrange the following three-dimensional objects in the descending order of their volumes:(i) A cuboid with dimensions 10 cm, 8 cm and 6 cm(ii) A cube of side 8 cm(iii) A cylinder with base radius 7 cm and height 7 cm(iv) A sphere of radius 7 cma)(i), (ii), (iii), (iv)b)(ii), (i), (iv), (iii)c)(iii), (ii), (i), (iv)d)(iv), (iii), (ii), (i)Correct answer is option 'D'. Can you explain this answer?.
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