You buy a sphere-shaped piece of chocolate that has a creamy center. The chocolate piece measures 1 inch in diameter. How much creamy filling can fit inside the chocolate piece? Calculate your answer using 3.14 for pi and round to the nearest tenth.(1 point)

inches3

1 answer

To find the amount of creamy filling that can fit inside the sphere-shaped piece of chocolate, we need to calculate the volume of the sphere.

The formula for the volume \( V \) of a sphere is:

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

where \( r \) is the radius of the sphere.

Given that the diameter of the chocolate piece is 1 inch, the radius \( r \) is:

\[ r = \frac{1}{2} = 0.5 \text{ inches} \]

Now we can substitute \( r \) into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times (0.5)^3 \]

Calculating \( (0.5)^3 \):

\[ (0.5)^3 = 0.125 \]

Now substitute this back into the volume formula:

\[ V = \frac{4}{3} \times 3.14 \times 0.125 \]

Calculating \( \frac{4 \times 3.14 \times 0.125}{3} \):

First, calculate \( 4 \times 3.14 \):

\[ 4 \times 3.14 = 12.56 \]

Next, multiply by \( 0.125 \):

\[ 12.56 \times 0.125 = 1.57 \]

Finally, divide by \( 3 \):

\[ V = \frac{1.57}{3} \approx 0.5233 \]

Rounding to the nearest tenth:

\[ V \approx 0.5 \]

Thus, the amount of creamy filling that can fit inside the chocolate piece is approximately:

\[ \boxed{0.5} \text{ inches}^3 \]