If a sphere has a radius of 3 cm, what is the volume of the sphere?

If a sphere has a radius of 3 cm, what is the volume of the sphere?

• A. 27π cm³
• B. 30π cm³
• C. 36π cm³
• D. 40π cm³

Answer: (A)

To find the volume of a sphere, the formula used is \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius of the sphere. In this case, the radius is given as 3 cm. First, we calculate \( r^3 \): \[ r^3 = 3^3 = 27 \] Next, we substitute this value into the volume formula: \[ V = \frac{4}{3} \pi (27) \] This simplifies to: \[ V = \frac{4 \times 27}{3} \pi = \frac{108}{3} \pi = 36 \pi \text{ cm}^3 \] Thus, the volume of the sphere is \( 36\pi \text{ cm}^3 \), which corresponds to the choice provided. This demonstrates that using the correct radius in the formula and performing the calculations accurately leads to the correct answer of \( 36\pi \text{ cm}^3 \).

To find the volume of a sphere, the formula used is ( V = \frac{4}{3} \pi r^3 ), where ( r ) is the radius of the sphere. In this case, the radius is given as 3 cm.

First, we calculate ( r^3 ):

[

r^3 = 3^3 = 27

]

Next, we substitute this value into the volume formula:

[

V = \frac{4}{3} \pi (27)

]

This simplifies to:

[

V = \frac{4 \times 27}{3} \pi = \frac{108}{3} \pi = 36 \pi \text{ cm}^3

]

Thus, the volume of the sphere is ( 36\pi \text{ cm}^3 ), which corresponds to the choice provided. This demonstrates that using the correct radius in the formula and performing the calculations accurately leads to the correct answer of ( 36\pi \text{ cm}^3 ).