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If each edge of a cube is doubled, its surface are will increase
- a)two times
- b)three times
- c)four times
- d)five times
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
If each edge of a cube is doubled, its surface are will increasea)two ...
Explanation:
When we double the edge of a cube, we are essentially multiplying the length of each edge by 2. Let the original edge length be l. After doubling the edge, new edge length will be 2l.
Calculating the surface area of the original cube:
The surface area of a cube is given by the formula 6l^2, where l is the length of an edge. Here, l is the original edge length. So, the surface area of the original cube is 6l^2.
Calculating the surface area of the doubled cube:
The surface area of the doubled cube is given by the formula 6(2l)^2, since each edge length is now 2l. Simplifying this expression, we get:
6(2l)^2 = 6(4l^2) = 24l^2
So, the surface area of the doubled cube is 24l^2.
Calculating the ratio of the surface areas:
To find the ratio of the surface areas, we need to divide the surface area of the doubled cube by the surface area of the original cube:
(24l^2) / (6l^2) = 4
So, the surface area of the doubled cube is 4 times the surface area of the original cube.
Conclusion:
Therefore, the correct option is C, that is, the surface area of the cube will increase four times if each edge of a cube is doubled.
When we double the edge of a cube, we are essentially multiplying the length of each edge by 2. Let the original edge length be l. After doubling the edge, new edge length will be 2l.
Calculating the surface area of the original cube:
The surface area of a cube is given by the formula 6l^2, where l is the length of an edge. Here, l is the original edge length. So, the surface area of the original cube is 6l^2.
Calculating the surface area of the doubled cube:
The surface area of the doubled cube is given by the formula 6(2l)^2, since each edge length is now 2l. Simplifying this expression, we get:
6(2l)^2 = 6(4l^2) = 24l^2
So, the surface area of the doubled cube is 24l^2.
Calculating the ratio of the surface areas:
To find the ratio of the surface areas, we need to divide the surface area of the doubled cube by the surface area of the original cube:
(24l^2) / (6l^2) = 4
So, the surface area of the doubled cube is 4 times the surface area of the original cube.
Conclusion:
Therefore, the correct option is C, that is, the surface area of the cube will increase four times if each edge of a cube is doubled.
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Community Answer
If each edge of a cube is doubled, its surface are will increasea)two ...
IF THE EDGE IS ONE TIME,THE SURFACE WILL BE TWO TIMES.NOW, IN THIS SITUATION THE EDGE IS DOUBLED SO,THE SURFACE AREA WILL ALSO DOUBLE.
PLEASE UPVOTE....THANK YOU!!
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If each edge of a cube is doubled, its surface are will increasea)two timesb)three timesc)four timesd)five timesCorrect answer is option 'C'. Can you explain this answer?
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