If the radius of a sphere is 4 cm, what is its volume?

• A. 201.06 cm³
• B. 268.08 cm³
• C. 50.27 cm³
• D. 75.36 cm³

Answer: (B)

To find the volume of a sphere, you can use the formula:

[

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

]

where (V) is the volume and (r) is the radius of the sphere. In this case, the radius is given as 4 cm.

First, calculate the radius cubed:

[

r^3 = 4^3 = 64 \text{ cm}^3

]

Next, substitute this value into the volume formula:

[

V = \frac{4}{3} \pi (64)

]

Now, calculate (\frac{4}{3} \times 64):

[

\frac{4 \times 64}{3} = \frac{256}{3} \approx 85.33 \text{ cm}^3

]

Now multiply by (\pi) (approximately 3.14):

[

V \approx 85.33 \times 3.14 \approx 268.08 \text{ cm}^3

]

This confirms that the volume of the sphere with a radius of 4 cm is indeed approximately 268.08 cm³.