Volume of Spheres Practice

Question

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Question
How much chocolate is in a spherical chocolate truffle with a radius of 12 mm? Use 3.14 as an approximation for pi. Round your answer to the nearest hundredth, if necessary.(1 point)
mm3
its not
7239.76

Answer 1

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

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

Where \( V \) is the volume, \( \pi \) is approximately 3.14, and \( r \) is the radius.

Given:

• Radius \( r = 12 \) mm
• \( \pi \approx 3.14 \)

Now, let's plug in the value:

\[ V = \frac{4}{3} \times 3.14 \times (12)^3 \]

First, calculate \( (12)^3 \):

\[ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 \]

Now substitute this back into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 1728 \]

Now calculate \( \frac{4}{3} \times 1728 \):

\[ \frac{4 \times 1728}{3} = \frac{6912}{3} = 2304 \]

Now multiply by \( 3.14 \):

\[ V = 3.14 \times 2304 \approx 7238.56 \]

Rounding to the nearest hundredth, the volume of the spherical chocolate truffle is:

\[ \text{Volume} \approx 7238.56 , \text{mm}^3 \]

So, your answer should be approximately 7238.56 mm³.