The length and the radius of a cylinder measured with slide callipers are found to be 4.54 em and 1.75 em respectively. Calculate the volume of the cylinder.

The correct option is 43.7 cm³.

To find the volume of a cylinder, we use the formula:
$V=\pi r^{2}l$
where $V$ is the volume, $r$ is the radius, and $l$ is the length (or height) of the cylinder.

Based on the measurements taken with the slide callipers:
Radius ($r$) = 1.75 cm (which has 3 significant figures)
Length ($l$) = 4.54 cm (which has 3 significant figures)

Substituting these values into the volume formula:
$V=\pi \times {\left(1.75\right)}^2\times 4.54$

$V=\pi \times 3.0625\times 4.54$

$V\approx 3.14159\times 13.90375$

$V\approx 43.68{\text{cm}}^3$

According to the rules of significant figures, the result of a multiplication must be rounded to the same number of significant figures as the measurement with the least number of significant figures. Since both the radius (1.75 cm) and the length (4.54 cm) have 3 significant figures, we round our final answer to 3 significant figures:
$V\approx 43.7{\text{cm}}^3$