Question

You buy a sphere-shaped 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 in terms of π and round to the nearest tenth.

__ inches^3

Answer 1

To find the volume of the creamy center inside the chocolate sphere, we first need to calculate the volume of a sphere using 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 chocolate sphere is 1 inch, we can find the radius:

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

Now, we can substitute the radius into the volume formula:

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

Calculating \( (0.5)^3 \):

\[
(0.5)^3 = 0.125
\]

Now, substituting back into the volume formula:

\[
V = \frac{4}{3} \pi (0.125)
\]

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

\[
\frac{4}{3} \times 0.125 = \frac{4 \times 0.125}{3} = \frac{0.5}{3} = \frac{1}{6}
\]

Thus, the volume of the chocolate sphere in terms of \( \pi \) is:

\[
V = \frac{1}{6} \pi \text{ cubic inches}
\]

Now, to find the numerical value, we can approximate \( \pi \) as \( 3.14 \):

\[
V \approx \frac{1}{6} \times 3.14 \approx 0.5233
\]

Now rounding to the nearest tenth, we have:

\[
V \approx 0.5 \text{ inches}^3
\]

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

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