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A solid cube is cut into two cuboids of equal volumes. Find the ratio of total surface area of given cube and that of one cuboid.
- a)3 : 2
- b)2 : 3
- c)3 : 1
- d)1 : 3
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
A solid cube is cut into two cuboids of equal volumes. Find the ratio ...
Volume of cuboid = a3/2 = Ibh
∴ Surface area of each cuboid
= 2 (lb + bh + lh)
= 2 (2a2) = 4a2
Total surface area of cube = 6a2
∴ Required ratio = 6a2 : 4a2 = 3 : 2
∴ Surface area of each cuboid
= 2 (lb + bh + lh)
= 2 (2a2) = 4a2
Total surface area of cube = 6a2
∴ Required ratio = 6a2 : 4a2 = 3 : 2
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Community Answer
A solid cube is cut into two cuboids of equal volumes. Find the ratio ...
To find the ratio of the total surface area of a given cube to that of one cuboid, we need to first understand the properties of a cube and a cuboid.
1. Understanding the properties of a cube:
- A cube is a three-dimensional shape with six identical square faces.
- All the edges of a cube are of equal length.
- The formula to find the total surface area of a cube is 6s^2, where s represents the length of one side of the cube.
2. Understanding the properties of a cuboid:
- A cuboid is a three-dimensional shape with six rectangular faces.
- The formula to find the total surface area of a cuboid is 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the cuboid respectively.
Now, let's solve the problem step by step:
Step 1: Let the length of the side of the cube be 's'.
Step 2: The volume of the cube is given by (side)^3 = s^3.
Step 3: Since the cube is cut into two cuboids of equal volumes, the volume of each cuboid will be (s^3)/2.
Step 4: Let the dimensions of one cuboid be l, w, and h.
Step 5: The volume of one cuboid is lwh = (s^3)/2.
Step 6: Since the volume of a cuboid is equal to the volume of the cube, we have lwh = s^3/2.
Step 7: Let's consider the total surface area of the cube as A and the total surface area of one cuboid as B.
Step 8: The total surface area of the cube is 6s^2 (as explained earlier).
Step 9: The total surface area of one cuboid is 2lw + 2lh + 2wh.
Step 10: From step 7, we have 6s^2 = B.
Step 11: From step 6, we have s^3/2 = lwh.
Step 12: Substituting s^3/2 = lwh in the equation 6s^2 = B, we get 6(s^3/2) = B.
Step 13: Simplifying, we have 3s^2 = B.
Step 14: Comparing the equations A = 6s^2 and B = 3s^2, we find that A:B = 6:3.
Step 15: Simplifying further, we get A:B = 2:1.
Therefore, the ratio of the total surface area of the given cube to that of one cuboid is 2:1, which is equivalent to option A (3:2).
1. Understanding the properties of a cube:
- A cube is a three-dimensional shape with six identical square faces.
- All the edges of a cube are of equal length.
- The formula to find the total surface area of a cube is 6s^2, where s represents the length of one side of the cube.
2. Understanding the properties of a cuboid:
- A cuboid is a three-dimensional shape with six rectangular faces.
- The formula to find the total surface area of a cuboid is 2lw + 2lh + 2wh, where l, w, and h represent the length, width, and height of the cuboid respectively.
Now, let's solve the problem step by step:
Step 1: Let the length of the side of the cube be 's'.
Step 2: The volume of the cube is given by (side)^3 = s^3.
Step 3: Since the cube is cut into two cuboids of equal volumes, the volume of each cuboid will be (s^3)/2.
Step 4: Let the dimensions of one cuboid be l, w, and h.
Step 5: The volume of one cuboid is lwh = (s^3)/2.
Step 6: Since the volume of a cuboid is equal to the volume of the cube, we have lwh = s^3/2.
Step 7: Let's consider the total surface area of the cube as A and the total surface area of one cuboid as B.
Step 8: The total surface area of the cube is 6s^2 (as explained earlier).
Step 9: The total surface area of one cuboid is 2lw + 2lh + 2wh.
Step 10: From step 7, we have 6s^2 = B.
Step 11: From step 6, we have s^3/2 = lwh.
Step 12: Substituting s^3/2 = lwh in the equation 6s^2 = B, we get 6(s^3/2) = B.
Step 13: Simplifying, we have 3s^2 = B.
Step 14: Comparing the equations A = 6s^2 and B = 3s^2, we find that A:B = 6:3.
Step 15: Simplifying further, we get A:B = 2:1.
Therefore, the ratio of the total surface area of the given cube to that of one cuboid is 2:1, which is equivalent to option A (3:2).
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A solid cube is cut into two cuboids of equal volumes. Find the ratio of total surface area of given cube and that of one cuboid.a)3 : 2b)2 : 3c)3 : 1d)1 : 3Correct answer is option 'A'. Can you explain this answer?
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