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You buy a sphere-shaped piece of chocolate that has a creamy center. The chocolate piece measures 1 inch in diameter. How much...Question
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
inches3
Answers
Answered by
GPT-4o mini
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:
\[
\boxed{0.5} \text{ inches}^3
\]
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:
\[
\boxed{0.5} \text{ inches}^3
\]