Question
The radius of a small ornament in the shape of a sphere is 2 inches. What is the approximate volume of the ornament? Use 3.14 for Pi. Round to the nearest tenth of a cubic inch.
Recall the formula V = four-thirds pi r cubed.
Inches cubed
Recall the formula V = four-thirds pi r cubed.
Inches cubed
Answers
GPT-4o mini
To calculate the volume \( V \) of a sphere, you can use the formula:
\[
V = \frac{4}{3} \pi r^3
\]
Given that the radius \( r \) is 2 inches and using \( \pi \approx 3.14 \), we can substitute the values into the formula.
1. Calculate \( r^3 \):
\[
r^3 = 2^3 = 2 \times 2 \times 2 = 8
\]
2. Substitute \( r^3 \) and \( \pi \) into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 8
\]
3. Multiply \( 3.14 \) and \( 8 \):
\[
3.14 \times 8 = 25.12
\]
4. Now multiply by \( \frac{4}{3} \):
\[
V = \frac{4}{3} \times 25.12 \approx 33.4933
\]
5. Finally, rounding to the nearest tenth:
\[
V \approx 33.5 \text{ cubic inches}
\]
Thus, the approximate volume of the ornament is \( \boxed{33.5} \) cubic inches.
\[
V = \frac{4}{3} \pi r^3
\]
Given that the radius \( r \) is 2 inches and using \( \pi \approx 3.14 \), we can substitute the values into the formula.
1. Calculate \( r^3 \):
\[
r^3 = 2^3 = 2 \times 2 \times 2 = 8
\]
2. Substitute \( r^3 \) and \( \pi \) into the volume formula:
\[
V = \frac{4}{3} \times 3.14 \times 8
\]
3. Multiply \( 3.14 \) and \( 8 \):
\[
3.14 \times 8 = 25.12
\]
4. Now multiply by \( \frac{4}{3} \):
\[
V = \frac{4}{3} \times 25.12 \approx 33.4933
\]
5. Finally, rounding to the nearest tenth:
\[
V \approx 33.5 \text{ cubic inches}
\]
Thus, the approximate volume of the ornament is \( \boxed{33.5} \) cubic inches.