Question
Use the image to answer the question.
A circle is traced along the circumference of a sphere at the center like a latitude. A dot is plotted at the center. The radius measures 3 centimeters.
Calculate the volume of the sphere using 3.14 for pi and round to the nearest tenth.
(1 point)
Responses
75.4 cm3
75.4 cm cubed
904.3 cm3
904.3 cm cubed
113.0 cm3
113.0 cm cubed
37.7 cm3
A circle is traced along the circumference of a sphere at the center like a latitude. A dot is plotted at the center. The radius measures 3 centimeters.
Calculate the volume of the sphere using 3.14 for pi and round to the nearest tenth.
(1 point)
Responses
75.4 cm3
75.4 cm cubed
904.3 cm3
904.3 cm cubed
113.0 cm3
113.0 cm cubed
37.7 cm3
Answers
Answered by
GPT-4o mini
To calculate the volume of a sphere, you can use the formula:
\[
V = \frac{4}{3} \pi r^3
\]
Where \( V \) is the volume and \( r \) is the radius of the sphere. In this case, the radius \( r \) is given as 3 centimeters, and we'll use \( \pi \approx 3.14 \).
First, calculate \( r^3 \):
\[
r^3 = 3^3 = 27
\]
Next, substitute the values into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 27
\]
Now perform the multiplication:
1. Calculate \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867 \quad (\text{approximation})
\]
2. Now multiply by 27:
\[
V \approx 4.1867 \times 27 \approx 113.04
\]
Finally, rounding \( 113.04 \) to the nearest tenth, we get:
\[
\approx 113.0 \text{ cm}^3
\]
Thus, the volume of the sphere is **113.0 cm³**.
\[
V = \frac{4}{3} \pi r^3
\]
Where \( V \) is the volume and \( r \) is the radius of the sphere. In this case, the radius \( r \) is given as 3 centimeters, and we'll use \( \pi \approx 3.14 \).
First, calculate \( r^3 \):
\[
r^3 = 3^3 = 27
\]
Next, substitute the values into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 27
\]
Now perform the multiplication:
1. Calculate \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867 \quad (\text{approximation})
\]
2. Now multiply by 27:
\[
V \approx 4.1867 \times 27 \approx 113.04
\]
Finally, rounding \( 113.04 \) to the nearest tenth, we get:
\[
\approx 113.0 \text{ cm}^3
\]
Thus, the volume of the sphere is **113.0 cm³**.