Differentials — Question 3

Question 3 - Solution

Let the surface area of the cube be: $$S = 6x^2$$ where $x$ is the length of a side.

(a) Approximate error using differentials:

$$dS = \frac{dS}{dx} \, dx = 12x \, dx$$ $$dS = 12(10)(0.2) = 24 \, \text{cm}^2$$

(b) Relative error: $$\frac{dS}{S} = \frac{24}{6(10)^2} = \frac{24}{600} = 0.04$$

Percentage error: $$0.04 \times 100 = \boxed{4\%}$$

Final Answer:

• Maximum error in surface area: $\boxed{24 \, \text{cm}^2}$

• Relative error: $\boxed{0.04}$

• Percentage error: $\boxed{4\%}$