Question

The error in the measurement of edge of cube is 2%. The maximum percentage error in the measurement of its surface area is ?

Answer 1

Answer:

A=24

Explanation:

A=6a2=6·22=24

Answer 2

Answer:

The maximum percentage error in the measurement of surface area when the error in the measurement is 2% is 4%.

Explanation:

Let ‘l’ be the length of the edge of a cube

According to the question, error in the

measurement of edge of cube is 2%.

→ (∆l/l) × 100 = 2%

We know that the lateral surface area of a cube is given as:

→ A = 4l²

Applying ‘log’ on both sides:

→ logA = log4 + logl²

→ logA = log4 + 2.logl

Differentiating on both sides:

→ dA/A = 2.dl/l

→ ∆A/A = 2.∆l/l

Now, the required error in the measurement of surface area is:

→ (∆A/A) × 100 = 2.(∆l/l) × 100

→ (∆A/A) × 100 = 2 × 2%

→ (∆A/A) × 100 = 4%

Therefore, the maximum percentage error in the measurement of surface area of the cube is 4%.

Shortcut:

The maximum percentage error in the measurement of surface area of cube when error in the measurement of edge is a% is 2a%.

The maximum percentage error in the measurement of volume of cube when error in the measurement of edge is a% is 3a%.

The maximum percentage error in the

measurement of volume of cube when

error in the measurement of surface area

of cube is a% is given as 1.5a%.