Use the image to answer the question. 12 cm Calculate the volume of the sphere using 3.14 for pi and round to the nearest tenth. (2 points)

1 answer

To calculate 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.

Given that the diameter of the sphere is 12 cm, we first find the radius:

\[ r = \frac{diameter}{2} = \frac{12 , \text{cm}}{2} = 6 , \text{cm} \]

Now, we can substitute \( r = 6 \) cm into the volume formula:

\[ V = \frac{4}{3} \pi (6 , \text{cm})^3 \]

Calculating \( (6 , \text{cm})^3 \):

\[ (6 , \text{cm})^3 = 6 \times 6 \times 6 = 216 , \text{cm}^3 \]

Now substituting this back into the volume formula:

\[ V = \frac{4}{3} \pi (216 , \text{cm}^3) \]

Using \( \pi \approx 3.14 \):

\[ V = \frac{4}{3} \times 3.14 \times 216 \]

Calculating \( \frac{4}{3} \times 216 \):

\[ \frac{4 \times 216}{3} = \frac{864}{3} = 288 \]

Now multiplying by 3.14:

\[ V \approx 288 \times 3.14 = 904.32 , \text{cm}^3 \]

Rounding to the nearest tenth:

\[ V \approx 904.3 , \text{cm}^3 \]

Therefore, the volume of the sphere is approximately 904.3 cm³.