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 in terms of π and round to the nearest tenth.
Answers
GPT-4o mini
To find out how much creamy filling 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 given by:
\[
V = \frac{4}{3} \pi r^3
\]
Where \( r \) is the radius of the sphere.
Given that the diameter of the chocolate piece is 1 inch, we can find the radius:
\[
r = \frac{\text{diameter}}{2} = \frac{1}{2} \text{ inch} = 0.5 \text{ inch}
\]
Now we can substitute the radius into the formula for volume:
\[
V = \frac{4}{3} \pi (0.5)^3
\]
Calculating \( (0.5)^3 \):
\[
(0.5)^3 = 0.125
\]
Now, substituting this back into the volume formula:
\[
V = \frac{4}{3} \pi (0.125)
\]
Now we perform the multiplication:
\[
\frac{4}{3} \times 0.125 = \frac{4 \times 0.125}{3} = \frac{0.5}{3} = \frac{1}{6}
\]
Thus, the volume of the sphere in terms of \( \pi \) is:
\[
V = \frac{1}{6} \pi
\]
To round this to the nearest tenth, we first approximate \( \pi \) as 3.14:
\[
\frac{1}{6} \times 3.14 \approx 0.5233
\]
Now rounding 0.5233 to the nearest tenth gives:
\[
0.5
\]
Thus, the total volume of creamy filling that can fit inside the chocolate piece, in terms of π, is:
\[
\frac{1}{6} \pi \text{ cubic inches}
\]
And rounding this to the nearest tenth, the volume of creamy filling that can fit inside is:
\[
\boxed{0.5} \text{ cubic inches}
\]
\[
V = \frac{4}{3} \pi r^3
\]
Where \( r \) is the radius of the sphere.
Given that the diameter of the chocolate piece is 1 inch, we can find the radius:
\[
r = \frac{\text{diameter}}{2} = \frac{1}{2} \text{ inch} = 0.5 \text{ inch}
\]
Now we can substitute the radius into the formula for volume:
\[
V = \frac{4}{3} \pi (0.5)^3
\]
Calculating \( (0.5)^3 \):
\[
(0.5)^3 = 0.125
\]
Now, substituting this back into the volume formula:
\[
V = \frac{4}{3} \pi (0.125)
\]
Now we perform the multiplication:
\[
\frac{4}{3} \times 0.125 = \frac{4 \times 0.125}{3} = \frac{0.5}{3} = \frac{1}{6}
\]
Thus, the volume of the sphere in terms of \( \pi \) is:
\[
V = \frac{1}{6} \pi
\]
To round this to the nearest tenth, we first approximate \( \pi \) as 3.14:
\[
\frac{1}{6} \times 3.14 \approx 0.5233
\]
Now rounding 0.5233 to the nearest tenth gives:
\[
0.5
\]
Thus, the total volume of creamy filling that can fit inside the chocolate piece, in terms of π, is:
\[
\frac{1}{6} \pi \text{ cubic inches}
\]
And rounding this to the nearest tenth, the volume of creamy filling that can fit inside is:
\[
\boxed{0.5} \text{ cubic inches}
\]