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Find the approximate change in total surface area of a cube of side x metre caused by increase in side by 1%.
- a)12 m2
- b)0.12x2 m2
- c)1.2x m2
- d)12x m2
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the approximate change in total surface area of a cube of side x ...
Toolbox:
Let y=f(x)
Δx denote a small increment in x
Δy=f(x+Δx)−f(x)
dy=(dy/dx)Δx
Surface area of cube =6s^2
Step 1:
The side of the cube =x meters
Decrease in side =1%
= 0.01x
Increase in side =Δx
= −0.01x
Step 2:
Surface area of cube = 6s^2
= 6 * x^2
S = 6x^2
ds/dx = 12x [Differentiating with respect to x]
Approximate change in surface area of cube = ds/dx * Δx
=12x *(0.01x)
= 0.12x^2 m^2
Most Upvoted Answer
Find the approximate change in total surface area of a cube of side x ...
Given, a cube of side x metre and increase in side by 1%.
The total surface area of a cube of side x metre is 6x2.
Increase in side = 1% of x = 0.01x
New side = x + 0.01x = 1.01x
New total surface area of the cube = 6(1.01x)2 = 6(1.0201x2) = 6.1206x2
Approximate change in total surface area = new total surface area - old total surface area
= 6.1206x2 - 6x2
= 0.1206x2
Therefore, the approximate change in total surface area of a cube of side x metre caused by an increase in side by 1% is 0.12x2 m2.
Hence, option (B) is the correct answer.
The total surface area of a cube of side x metre is 6x2.
Increase in side = 1% of x = 0.01x
New side = x + 0.01x = 1.01x
New total surface area of the cube = 6(1.01x)2 = 6(1.0201x2) = 6.1206x2
Approximate change in total surface area = new total surface area - old total surface area
= 6.1206x2 - 6x2
= 0.1206x2
Therefore, the approximate change in total surface area of a cube of side x metre caused by an increase in side by 1% is 0.12x2 m2.
Hence, option (B) is the correct answer.
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