Question

the error in measurement of side of a cube is 2% find percentage error in measurement of its volume and surface area.
​

Answer 1

Answer:

Let the side of cube be 10 units, then volume of this cube 1000 cubic units

Now, there is a 2% error in measuring the volume, which means volume is either measured 2% less or it is measured 2% more.

2% of 1000 is 20.

So, the volume measured is either 980 or 1020

If the measured volume is 980 the measured size of this cube is 9.93288 which is 0.067 units less than the original size of 10 units. So percentage error is (0.067/10)*100 = 0.67% approx

If the measured volume is 1020 the measured size of the cube is 10.0662271 which is 0.0662271 units more than the original size of 10 units. So percentage error is (0.066/10)*100 = 0.66% approx

So we see that the error in the measurement of the side of the cube will approximately lie between 0.66% to 0.67%