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The lateral surface area of a cube is 256 m2 The volume of the cube is
- a)64 m3.
- b)512 m3.
- c)216 m3.
- d)256 m3.
Correct answer is option 'B'. Can you explain this answer?
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The lateral surface area of a cube is 256m2 The volume of the cube isa...
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The lateral surface area of a cube is 256m2 The volume of the cube isa...
Lateral surface area of cube = 4L^2
256=4L^2
256/4=L^2
64=l^2
√64=L
L= 8
Volume of cube=L^3
=8×8×8
=512m^3
256=4L^2
256/4=L^2
64=l^2
√64=L
L= 8
Volume of cube=L^3
=8×8×8
=512m^3
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The lateral surface area of a cube is 256m2 The volume of the cube isa...
Lateral Surface Area of a Cube:
The lateral surface area of a cube refers to the total area of all the faces of the cube excluding the top and bottom faces. In a cube, all the faces are identical squares, so the lateral surface area can be calculated by multiplying the length of one side of the square face by the number of faces, which is 4 in the case of a cube.
Given Information:
The lateral surface area of the cube is given as 256 m2.
Calculation of Side Length:
Let's assume the side length of the cube is 'a'.
Since the cube has 6 faces, out of which 4 are lateral faces, the lateral surface area can be calculated as:
Lateral Surface Area = 4 * (side length)^2
Given that the lateral surface area is 256 m2, we can write the equation as:
256 = 4 * (a)^2
Simplifying the equation, we get:
(a)^2 = 64
Taking the square root of both sides, we find:
a = 8
Calculation of Volume:
The volume of a cube is given by the formula:
Volume = (side length)^3
Substituting the value of 'a' as 8, we can calculate the volume as:
Volume = (8)^3
Volume = 512 m3
Therefore, the correct answer is option B) 512 m3.
The lateral surface area of a cube refers to the total area of all the faces of the cube excluding the top and bottom faces. In a cube, all the faces are identical squares, so the lateral surface area can be calculated by multiplying the length of one side of the square face by the number of faces, which is 4 in the case of a cube.
Given Information:
The lateral surface area of the cube is given as 256 m2.
Calculation of Side Length:
Let's assume the side length of the cube is 'a'.
Since the cube has 6 faces, out of which 4 are lateral faces, the lateral surface area can be calculated as:
Lateral Surface Area = 4 * (side length)^2
Given that the lateral surface area is 256 m2, we can write the equation as:
256 = 4 * (a)^2
Simplifying the equation, we get:
(a)^2 = 64
Taking the square root of both sides, we find:
a = 8
Calculation of Volume:
The volume of a cube is given by the formula:
Volume = (side length)^3
Substituting the value of 'a' as 8, we can calculate the volume as:
Volume = (8)^3
Volume = 512 m3
Therefore, the correct answer is option B) 512 m3.
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The lateral surface area of a cube is 256m2 The volume of the cube isa)64 m3.b)512 m3.c)216 m3.d)256 m3.Correct answer is option 'B'. Can you explain this answer?
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