What is the volume (in cm³) of a solid sphere whose radius is 2.1 cm (rounded off to two decimal places)? (Use π =22/7 )

The correct option is 38.81.

To find the volume of a solid sphere, we use the standard formula for the volume of a sphere:

$$V=\frac{4}{3}\pi r^3$$

Where:
- $V$ is the volume of the sphere.
- $r$ is the radius of the sphere.
- $\pi$ is a mathematical constant, given as $\frac{22}{7}$.

Given that the radius $r=2.1\text{cm}$, we can substitute these values into the formula:

$$V=\frac{4}{3}\times \frac{22}{7}\times {\left(2.1\right)}^3$$

Expanding the cube of the radius:

$$V=\frac{4}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1$$

We can simplify the expression by combining terms. Since $3\times 7=21$ in the denominator, and we have $2.1$ in the numerator, we get:

$$\frac{2.1}{21}=0.1$$

Substituting this back into the volume equation simplifies it to:

$$V=4\times 22\times 0.1\times 2.1\times 2.1$$

Now, let us calculate the product step-by-step:

$$4\times 22=88$$

$$88\times 0.1=8.8$$

$$2.1\times 2.1=4.41$$

Multiplying these results together:

$$V=8.8\times 4.41=38.808{\text{cm}}^3$$

Rounding off the final value to two decimal places, we examine the third decimal digit (which is 8). Since this digit is 5 or greater, we round up the second decimal place from 0 to 1:

$$V\approx 38.81{\text{cm}}^3$$

Therefore, the volume of the solid sphere is 38.81 cm³.