Question

If the diameter of a cylinder is $\text{12.6}\pm\text{0.1} \, cm$ and its height is $34.2\pm0.1 \, cm$ , then find the volume of the cylinder to the nearest significant figure.

• A. $4264.4\pm81 \, cm^{3}$
• B. $4260\pm81 \, cm^{3}$
• C. $4300\pm80 \, cm^{3}$
• D. $4260\pm80 \, cm^{3}$

Answer 1

Answer: (D)

$V =\frac{\pi d ^2 h }{4}=\frac{\pi}{4}(12.6)^2(34.2) cm ^3$
$\frac{dV}{V}=\frac{2 d \left(d\right)}{d}+\frac{d \left(h\right)}{h}$
Converting to errors,
$\frac{\Delta V}{V}=2\frac{\Delta d}{d}+\frac{\Delta h}{h}$
$\frac{\Delta V}{4260}=2\left(\frac{0.1}{12.6}\right)+\left(\frac{0.1}{34.2}\right)$
$\Rightarrow \Delta V=80 \, cm^{3}$
$V=4260\pm80cm^{3}$