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The edges of a cuboid are in the ratio 2 : 3 : 4. If the total surface area of the cuboid is 468 sq cm, what is its volume?
- a)640 cubic cm
- b)650 cubic cm
- c)658 cubic cm
- d)648 cubic cm
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The edges of a cuboid are in the ratio 2 : 3 : 4. If the total surface...
Let it's edges are 2x, 3x, 4x
Surface area = 468
Most Upvoted Answer
The edges of a cuboid are in the ratio 2 : 3 : 4. If the total surface...
Given:
- The edges of the cuboid are in the ratio 2:3:4.
- The total surface area of the cuboid is 468 sq cm.
To find:
- The volume of the cuboid.
Solution:
Let's assume the three edges of the cuboid to be 2x, 3x, and 4x.
Step 1: Finding the Surface Area:
The total surface area of a cuboid is given by the formula:
2 (lw + lh + wh)
Given that the total surface area is 468 sq cm, we can write the equation as:
2(2x * 3x + 2x * 4x + 3x * 4x) = 468
Simplifying the equation:
2(6x^2 + 8x^2 + 12x^2) = 468
2(26x^2) = 468
52x^2 = 468
x^2 = 468/52
x^2 = 9
x = √9
x = 3
Therefore, the three edges of the cuboid are 2x = 2 * 3 = 6, 3x = 3 * 3 = 9, and 4x = 4 * 3 = 12.
Step 2: Finding the Volume:
The volume of a cuboid is given by the formula:
lwh
Substituting the values, we have:
Volume = 6 * 9 * 12
Volume = 648 cubic cm
Therefore, the volume of the cuboid is 648 cubic cm, which is option D.
- The edges of the cuboid are in the ratio 2:3:4.
- The total surface area of the cuboid is 468 sq cm.
To find:
- The volume of the cuboid.
Solution:
Let's assume the three edges of the cuboid to be 2x, 3x, and 4x.
Step 1: Finding the Surface Area:
The total surface area of a cuboid is given by the formula:
2 (lw + lh + wh)
Given that the total surface area is 468 sq cm, we can write the equation as:
2(2x * 3x + 2x * 4x + 3x * 4x) = 468
Simplifying the equation:
2(6x^2 + 8x^2 + 12x^2) = 468
2(26x^2) = 468
52x^2 = 468
x^2 = 468/52
x^2 = 9
x = √9
x = 3
Therefore, the three edges of the cuboid are 2x = 2 * 3 = 6, 3x = 3 * 3 = 9, and 4x = 4 * 3 = 12.
Step 2: Finding the Volume:
The volume of a cuboid is given by the formula:
lwh
Substituting the values, we have:
Volume = 6 * 9 * 12
Volume = 648 cubic cm
Therefore, the volume of the cuboid is 648 cubic cm, which is option D.
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The edges of a cuboid are in the ratio 2 : 3 : 4. If the total surface area of the cuboid is 468 sq cm, what is its volume?a)640 cubic cmb)650 cubic cmc)658 cubic cmd)648 cubic cmCorrect answer is option 'D'. Can you explain this answer?
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