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Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?
- a)455 cm3
- b)460 cm3
- c)450 cm3
- d)425 cm3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Two boxes have the same height, equal to 35 cm. One box has a square ...
Required Difference = Volume of cylinder - volume of cuboid
= πr2h - lbh
= 22/7 x 6 x 6 x 35 - 35 x 10 x 10
= 3960 - 3500 = 460 cm3
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Two boxes have the same height, equal to 35 cm. One box has a square ...
Volume of the Square Box
To find the volume of the square box, we use the formula for the volume of a rectangular prism:
- Volume = Base Area × Height
- Base Area = Side Length × Side Length
- Side Length = 10 cm
- Height = 35 cm
Calculating the base area:
- Base Area = 10 cm × 10 cm = 100 cm²
Now, calculating the volume:
- Volume = 100 cm² × 35 cm = 3500 cm³
Volume of the Cylindrical Box
To find the volume of the cylindrical box, we use the formula for the volume of a cylinder:
- Volume = π × (Radius)² × Height
- Diameter = 12 cm, so Radius = Diameter / 2 = 6 cm
- Height = 35 cm
Calculating the volume:
- Volume = π × (6 cm)² × 35 cm
- Volume = π × 36 cm² × 35 cm
- Volume = 1260π cm³ (Using π ≈ 3.14)
- Volume ≈ 1260 × 3.14 ≈ 3962.4 cm³
Difference in Volumes
Now, we find the difference in volumes between the cylindrical and square boxes:
- Difference = Volume of Cylinder - Volume of Square Box
- Difference ≈ 3962.4 cm³ - 3500 cm³
- Difference ≈ 462.4 cm³
To round this to the nearest whole number, we find that the difference is approximately 460 cm³.
Thus, the correct answer is option 'B': 460 cm³.
To find the volume of the square box, we use the formula for the volume of a rectangular prism:
- Volume = Base Area × Height
- Base Area = Side Length × Side Length
- Side Length = 10 cm
- Height = 35 cm
Calculating the base area:
- Base Area = 10 cm × 10 cm = 100 cm²
Now, calculating the volume:
- Volume = 100 cm² × 35 cm = 3500 cm³
Volume of the Cylindrical Box
To find the volume of the cylindrical box, we use the formula for the volume of a cylinder:
- Volume = π × (Radius)² × Height
- Diameter = 12 cm, so Radius = Diameter / 2 = 6 cm
- Height = 35 cm
Calculating the volume:
- Volume = π × (6 cm)² × 35 cm
- Volume = π × 36 cm² × 35 cm
- Volume = 1260π cm³ (Using π ≈ 3.14)
- Volume ≈ 1260 × 3.14 ≈ 3962.4 cm³
Difference in Volumes
Now, we find the difference in volumes between the cylindrical and square boxes:
- Difference = Volume of Cylinder - Volume of Square Box
- Difference ≈ 3962.4 cm³ - 3500 cm³
- Difference ≈ 462.4 cm³
To round this to the nearest whole number, we find that the difference is approximately 460 cm³.
Thus, the correct answer is option 'B': 460 cm³.
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Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?a)455 cm3b)460 cm3c)450 cm3d)425 cm3Correct answer is option 'B'. Can you explain this answer?
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Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?a)455 cm3b)460 cm3c)450 cm3d)425 cm3Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?a)455 cm3b)460 cm3c)450 cm3d)425 cm3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?a)455 cm3b)460 cm3c)450 cm3d)425 cm3Correct answer is option 'B'. Can you explain this answer?.
Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?a)455 cm3b)460 cm3c)450 cm3d)425 cm3Correct answer is option 'B'. Can you explain this answer? for Railways 2024 is part of Railways preparation. The Question and answers have been prepared according to the Railways exam syllabus. Information about Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?a)455 cm3b)460 cm3c)450 cm3d)425 cm3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Railways 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two boxes have the same height, equal to 35 cm. One box has a square base of 10 cm. The other box is cylindrical, and the diameter of its base is 12 cm. What is the difference in their volumes?a)455 cm3b)460 cm3c)450 cm3d)425 cm3Correct answer is option 'B'. Can you explain this answer?.
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