Question

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

• A. $4264.4\pm 81c{m}^3$
• B. $4260\pm 81c{m}^3$
• C. $4300\pm 80c{m}^3$
• D. $4260\pm 80c{m}^3$

Answer 1

Answer: (D)

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