Question

The side of a cube is $(2.00 \pm 0.01)\, cm$. The volume and surface area of cube are, respectively,

• A. $\left(8.00 \pm 0.12\right)\,cm^{3}$, $\left(24.0 \pm 0.24\right)\,cm^{2}$
• B. $\left(8.00 \pm 0.01\right)\,cm^{3}$, $\left(24.0 \pm 0.01\right)\,cm^{2}$
• C. $\left(8.00 \pm 0.04\right)\,cm^{3}$, $\left(24.0 \pm 0.06\right)\,cm^{2}$
• D. $\left(8.00 \pm 0.03\right)\,cm^{3}$, $\left(24.0 \pm 0.02\right)\,cm^{2}$

Answer 1

Answer: (A)

Volume, $V= a^3 = 8.00 \,cm^3$. Also,
$\frac{\Delta V}{V}=3 \frac{\Delta a}{a}$
$\Rightarrow \Delta V=3V\left(\frac{\Delta a}{a}\right)=\left(3\right)\left(8.00\right)\left(\frac{0.01}{2.00}\right)=0.12\,cm^{2}$
Therefore, $V=\left(8.00\pm0.12\right)cm^{2}$
Also, $\frac{\Delta A}{A}=2 \frac{\Delta a}{a}$
$\Rightarrow \Delta A=2A\left(\frac{\Delta a}{a}\right)=2\left(24.0\right)\left(\frac{0.01}{2.00}\right)=0.24\,cm^{2}$
Therefore, $A=\left(24.0\pm0.24\right)cm^{2}$