if each edge of a cube is increased by 50%, find the percentage increase in its surface area
Answers
Answer:
125 %
Step-By-Step Explanation:
In such questions, the first step of all individuals should be assuming the side to be a variable.
Let the measure of each edge of the cube be ' x ' cm.
Total surface area of the cube = 6 ( x ) ^ 2
Total surface area of the cube = 6 * x ^ 2
Total surface area of the cube = 6x ^ 2 cm²
Now when each edge is increased by 50 %,
Measure of the edge of new cube = x + 50 % of x
Measure of the edge of new cube = x + 50x / 100
Measure of the edge of new cube = x + x / 2
Measure of the edge of new cube = ( 3x / 2 ) cm
Total surface area of the new cube = 6 * ( 3x / 2 ) ^ 2
Total surface area of the new cube = 6 * ( 9x^2 / 4 )
Total surface area of the new cube = 54x ^ 2 / 4
Total surface area of the new cube = 13.5 x ^ 2 cm²
Increase in the total surface area = 13.5 x ^ 2 - 6 x ^ 2
Increase in the total surface area = 7.5 x ^ 2 cm²
Now,
Percentage increase in the total surface area = ( Increase in total surface area * 100 ) / Initial total surface area of the cube
Percentage increase in the total surface area = ( 7.5 x ^ 2 * 100 ) / 6 x ^ 2
Percentage increase in the total surface area = 750 x ^ 2 / 6 x ^ 2
Percentage increase in the total surface area = 750 / 6
Percentage increase in the total surface area = 375 / 3
Percentage increase in the total surface area = 125 %