If a sphere has a diameter of 10 cm, what is its volume in cubic cm?

If a sphere has a diameter of 10 cm, what is its volume in cubic cm?

• A. 523.6
• B. 314.15
• C. 416.67
• D. 784.82

Answer: (A)

To determine the volume of a sphere, the formula used is \( V = \frac{4}{3} \pi r^3 \), where \( r \) is the radius of the sphere. Given that the diameter of the sphere is 10 cm, the radius \( r \) can be calculated by dividing the diameter by 2. Therefore, the radius is \( r = \frac{10}{2} = 5 \) cm. Now, substituting this radius into the volume formula: \[ V = \frac{4}{3} \pi (5)^3 \] Calculating \( (5)^3 \) gives \( 125 \), so: \[ V = \frac{4}{3} \pi \times 125 \] This simplifies to: \[ V = \frac{500}{3} \pi \] Using the approximation \( \pi \approx 3.1416 \): \[ V \approx \frac{500}{3} \times 3.1416 \approx 523.6 \text{ cubic cm} \] Thus, the volume of the sphere is approximately 523.6 cubic cm. This is why the answer

To determine the volume of a sphere, the formula used is ( V = \frac{4}{3} \pi r^3 ), where ( r ) is the radius of the sphere.

Given that the diameter of the sphere is 10 cm, the radius ( r ) can be calculated by dividing the diameter by 2. Therefore, the radius is ( r = \frac{10}{2} = 5 ) cm.

Now, substituting this radius into the volume formula:

[

V = \frac{4}{3} \pi (5)^3

]

Calculating ( (5)^3 ) gives ( 125 ), so:

[

V = \frac{4}{3} \pi \times 125

]

This simplifies to:

[

V = \frac{500}{3} \pi

]

Using the approximation ( \pi \approx 3.1416 ):

[

V \approx \frac{500}{3} \times 3.1416 \approx 523.6 \text{ cubic cm}

]

Thus, the volume of the sphere is approximately 523.6 cubic cm. This is why the answer