The radius of a sphere is 1.41 em. Express its volume to an appropriate number of significant figures.

The correct option is 11.7 cm³.

To find the volume of the sphere, we use the standard formula for the volume of a sphere:
$$V=\frac{4}{3}\pi r^3$$
where r is the radius of the sphere.

The given radius is r = 1.41 cm (noting that "em" in the question text is a typographical error for "cm", as confirmed by the units in the options). The value 1.41 has three significant figures.

Substituting the radius into the volume formula:
$$V=\frac{4}{3}\times \pi \times (1.41{)}^3$$
First, calculate the cube of the radius:
$$(1.41{)}^3\approx 2.803221$$
Now, multiply by π (approximately 3.14159) and by 4/3:
$$V\approx 1.33333\times 3.14159\times 2.803221\approx 11.742{\text{cm}}^3$$

When multiplying or dividing numbers, the final result must be rounded to the same number of significant figures as the measurement with the fewest significant figures. Since the given radius (1.41 cm) has 3 significant figures, the calculated volume must be rounded to 3 significant figures.

Rounding 11.742 cm³ to 3 significant figures gives 11.7 cm³.