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The volume of a cube with surface area 384 sq. cm, is :
- a)216 cm3
- b)256 cm3
- c)484 cm3
- d)512 cm3
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
The volume of a cube with surface area 384 sq. cm, is :a)216 cm3b)256c...
The surface area of a cube is given by 6 times the area of one face, and the area of a face of a cube is equal to the length of one edge squared. So if the surface area of the cube is 384 cm^2, we can write the equation:
6 * edge^2 = 384
Solving for the edge length:
edge^2 = 64
edge = 8
The volume of a cube is equal to the length of one edge cubed, so the volume of this cube is:
volume = 8^3 = 512 cm^3
Most Upvoted Answer
The volume of a cube with surface area 384 sq. cm, is :a)216 cm3b)256c...
The volume of a cube with a surface area of 384 sq. cm is 512 cm3, which corresponds to option D.
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The volume of a cube with surface area 384 sq. cm, is :a)216 cm3b)256c...
Given:
Surface area of the cube = 384 sq. cm
To find:
Volume of the cube
Solution:
To find the volume, we need to know the length of one side of the cube.
Step 1: Find the length of one side of the cube
Since the cube has 6 equal faces, we can find the length of one side by dividing the surface area by 6.
Surface area of the cube = 6 * (side)^2
384 = 6 * (side)^2
Dividing both sides by 6:
(side)^2 = 384/6
(side)^2 = 64
Taking the square root of both sides:
side = √64
side = 8 cm
Step 2: Find the volume of the cube
Volume of the cube = (side)^3
Volume = (8)^3
Volume = 512 cm^3
Therefore, the volume of the cube with a surface area of 384 sq. cm is 512 cm^3.
Hence, the correct answer is option D) 512 cm^3.
Surface area of the cube = 384 sq. cm
To find:
Volume of the cube
Solution:
To find the volume, we need to know the length of one side of the cube.
Step 1: Find the length of one side of the cube
Since the cube has 6 equal faces, we can find the length of one side by dividing the surface area by 6.
Surface area of the cube = 6 * (side)^2
384 = 6 * (side)^2
Dividing both sides by 6:
(side)^2 = 384/6
(side)^2 = 64
Taking the square root of both sides:
side = √64
side = 8 cm
Step 2: Find the volume of the cube
Volume of the cube = (side)^3
Volume = (8)^3
Volume = 512 cm^3
Therefore, the volume of the cube with a surface area of 384 sq. cm is 512 cm^3.
Hence, the correct answer is option D) 512 cm^3.
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The volume of a cube with surface area 384 sq. cm, is :a)216 cm3b)256cm3c)484cm3d)512cm3Correct answer is option 'D'. Can you explain this answer?
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