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If each edge of a cube is increased by 50%, find the percentage increase in its surface area.
- a)125%
- b)150%
- c)175%
- d)110%
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If each edge of a cube is increased by 50%, find the percentage increa...
Given:
If each edge of a cube is increased by 50%.
We know that,
The surface area of cube = 6 side2
So,
According to the question,
Let the side of the cube be x.
Each side of the cube increased by 50%.
So,
= (x)(100+50))/100
= 1.5x
The surface area of the cube = 6x2
The new surface area of the cube (side =1.5x) = 6 x 2.25x2
Increase percentage in the surface area = ((6 x 2.25x2-6x2)/6x2) x 100
= 125%
∴ The percentage increase in the surface area is 125%.
If each edge of a cube is increased by 50%.
We know that,
The surface area of cube = 6 side2
So,
According to the question,
Let the side of the cube be x.
Each side of the cube increased by 50%.
So,
= (x)(100+50))/100
= 1.5x
The surface area of the cube = 6x2
The new surface area of the cube (side =1.5x) = 6 x 2.25x2
Increase percentage in the surface area = ((6 x 2.25x2-6x2)/6x2) x 100
= 125%
∴ The percentage increase in the surface area is 125%.
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Community Answer
If each edge of a cube is increased by 50%, find the percentage increa...
Calculation of Percentage Increase in Surface Area of Cube:
Increasing each edge of a cube by 50% means that each edge is multiplied by 1.5. Let the original edge length be 'x'. After the increase, the new edge length would be 1.5x.
Calculation of Surface Area:
The surface area of a cube is given by the formula: 6 * (side length)^2.
So, the original surface area = 6 * x^2
And, the new surface area = 6 * (1.5x)^2 = 6 * 2.25x^2 = 13.5x^2.
Calculation of Percentage Increase:
To find the percentage increase in surface area, we need to calculate the difference between the new and original surface areas, divide it by the original surface area, and then multiply by 100.
Percentage Increase = ((New Surface Area - Original Surface Area) / Original Surface Area) * 100
= ((13.5x^2 - 6x^2) / 6x^2) * 100
= (7.5x^2 / 6x^2) * 100
= 1.25 * 100
= 125%
Therefore, the percentage increase in the surface area of the cube when each edge is increased by 50% is 125%. Hence, option 'A' is the correct answer.
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If each edge of a cube is increased by 50%, find the percentage increase in its surface area.a)125%b)150%c)175%d)110%Correct answer is option 'A'. Can you explain this answer?
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