Question

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

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

Answer 1

Answer: (A)

Volume, $V=a^3=8.00c{m}^3$. Also,
$\frac{ΔV}{V}=3\frac{Δa}{a}$
$⇒ΔV=3V\left(\frac{Δa}{a}\right)=\left(3\right)\left(8.00\right)\left(\frac{0.01}{2.00}\right)=0.12c{m}^2$
Therefore, $V=\left(8.00Â\pm 0.12\right)c{m}^2$
Also, $\frac{ΔA}{A}=2\frac{Δa}{a}$
$⇒ΔA=2A\left(\frac{Δa}{a}\right)=2\left(24.0\right)\left(\frac{0.01}{2.00}\right)=0.24c{m}^2$
Therefore, $A=\left(24.0Â\pm 0.24\right)c{m}^2$