If the radius of a sphere is 8 cm, what is the volume in cubic cm?

If the radius of a sphere is 8 cm, what is the volume in cubic cm?

• A. 0.214
• B. 2.144
• C. 21.44
• D. 2,144

Answer: (D)

To calculate the volume of a sphere, the formula used is \( V = \frac{4}{3} \pi r^3 \), where \( V \) is the volume and \( r \) is the radius of the sphere. In this case, the radius is given as 8 cm. Plugging this value into the formula gives: \[ V = \frac{4}{3} \pi (8)^3 \] Calculating \( (8)^3 \) yields 512. Therefore, the equation for the volume becomes: \[ V = \frac{4}{3} \pi (512) \] Next, calculating \( \frac{4}{3} \times 512 \) results in approximately 681.33. Then, multiplying this by \( \pi \) (approximately 3.14) gives: \[ V \approx 681.33 \times 3.14 \approx 2,138.23 \] When rounded or adjusted for significant figures, this value aligns closely with the choice of 2,144 cubic cm, making it the correct answer. Understanding this calculation demonstrates how to apply the volume formula for a sphere effectively, reinforcing foundational concepts

To calculate the volume of a sphere, the formula used is ( 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 8 cm. Plugging this value into the formula gives:

[

V = \frac{4}{3} \pi (8)^3

]

Calculating ( (8)^3 ) yields 512. Therefore, the equation for the volume becomes:

[

V = \frac{4}{3} \pi (512)

]

Next, calculating ( \frac{4}{3} \times 512 ) results in approximately 681.33. Then, multiplying this by ( \pi ) (approximately 3.14) gives:

[

V \approx 681.33 \times 3.14 \approx 2,138.23

]

When rounded or adjusted for significant figures, this value aligns closely with the choice of 2,144 cubic cm, making it the correct answer.

Understanding this calculation demonstrates how to apply the volume formula for a sphere effectively, reinforcing foundational concepts