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The edges of a cuboid are in the ratio 4 : 3 : 2 and the volume of the cuboid is 648 cubic cm. What is the surface area of the cuboid?
- a)468sq.cm
- b)446sq.cm
- c)424sq.cm
- d)436sq.cm
Correct answer is option 'A'. Can you explain this answer?
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The edges of a cuboid are in the ratio 4 : 3 : 2 and the volume of the...
Given information:
- The edges of the cuboid are in the ratio 4:3:2.
- The volume of the cuboid is 648 cubic cm.
To find:
- The surface area of the cuboid.
Solution:
Step 1: Determine the dimensions of the cuboid
Let the edges of the cuboid be 4x, 3x, and 2x.
Step 2: Find the volume of the cuboid
The volume of a cuboid is given by the formula V = l × b × h, where l, b, and h are the length, breadth, and height of the cuboid, respectively.
Given that the volume of the cuboid is 648 cubic cm, we have:
4x × 3x × 2x = 648
24x^3 = 648
x^3 = 27
Taking the cube root on both sides, we get:
x = 3
Therefore, the dimensions of the cuboid are:
Length = 4x = 4 × 3 = 12 cm
Breadth = 3x = 3 × 3 = 9 cm
Height = 2x = 2 × 3 = 6 cm
Step 3: Find the surface area of the cuboid
The surface area of a cuboid is given by the formula SA = 2(lb + bh + lh), where l, b, and h are the length, breadth, and height of the cuboid, respectively.
Substituting the values, we have:
SA = 2(12 × 9 + 9 × 6 + 12 × 6)
SA = 2(108 + 54 + 72)
SA = 2(234)
SA = 468
Therefore, the surface area of the cuboid is 468 square cm.
Hence, the correct answer is option A) 468 sq.cm.
- The edges of the cuboid are in the ratio 4:3:2.
- The volume of the cuboid is 648 cubic cm.
To find:
- The surface area of the cuboid.
Solution:
Step 1: Determine the dimensions of the cuboid
Let the edges of the cuboid be 4x, 3x, and 2x.
Step 2: Find the volume of the cuboid
The volume of a cuboid is given by the formula V = l × b × h, where l, b, and h are the length, breadth, and height of the cuboid, respectively.
Given that the volume of the cuboid is 648 cubic cm, we have:
4x × 3x × 2x = 648
24x^3 = 648
x^3 = 27
Taking the cube root on both sides, we get:
x = 3
Therefore, the dimensions of the cuboid are:
Length = 4x = 4 × 3 = 12 cm
Breadth = 3x = 3 × 3 = 9 cm
Height = 2x = 2 × 3 = 6 cm
Step 3: Find the surface area of the cuboid
The surface area of a cuboid is given by the formula SA = 2(lb + bh + lh), where l, b, and h are the length, breadth, and height of the cuboid, respectively.
Substituting the values, we have:
SA = 2(12 × 9 + 9 × 6 + 12 × 6)
SA = 2(108 + 54 + 72)
SA = 2(234)
SA = 468
Therefore, the surface area of the cuboid is 468 square cm.
Hence, the correct answer is option A) 468 sq.cm.
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The edges of a cuboid are in the ratio 4 : 3 : 2 and the volume of the cuboid is 648 cubic cm. What is the surface area of the cuboid?a)468sq.cmb)446sq.cmc)424sq.cmd)436sq.cmCorrect answer is option 'A'. Can you explain this answer?
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