Question
Joshua and Isabella are having a snowball fight. Joshua has a snowball, shaped as a sphere, with a radius of 6 cm. Isabella also has spherical snowball with a radius of 3 cm. Find the volume of each snowball (use 3.14 for ). Then, complete the following statement, and round the answer to the nearest hundredth, if necessary.
Answers
GPT-4o mini
To find the volume of each snowball, we will use the formula for the volume of a sphere, which is given by:
\[
V = \frac{4}{3} \pi r^3
\]
Where \( V \) is the volume and \( r \) is the radius.
### Volume of Joshua's Snowball
Joshua's snowball has a radius of \( 6 \) cm:
\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]
Calculating \( (6)^3 = 216 \):
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Now, calculating \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]
Now, we can calculate:
\[
V \approx 4.1867 \times 216 \approx 903.8372
\]
Rounding to the nearest hundredth:
\[
V \approx 903.84 \text{ cm}^3
\]
### Volume of Isabella's Snowball
Isabella's snowball has a radius of \( 3 \) cm:
\[
V = \frac{4}{3} \times 3.14 \times (3)^3
\]
Calculating \( (3)^3 = 27 \):
\[
V = \frac{4}{3} \times 3.14 \times 27
\]
Calculating \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]
Now, we can calculate:
\[
V \approx 4.1867 \times 27 \approx 112.99
\]
Rounding to the nearest hundredth:
\[
V \approx 112.99 \text{ cm}^3
\]
### Complete the Statement
Joshua's snowball has a volume of **903.84 cm³**, while Isabella's snowball has a volume of **112.99 cm³**.
\[
V = \frac{4}{3} \pi r^3
\]
Where \( V \) is the volume and \( r \) is the radius.
### Volume of Joshua's Snowball
Joshua's snowball has a radius of \( 6 \) cm:
\[
V = \frac{4}{3} \times 3.14 \times (6)^3
\]
Calculating \( (6)^3 = 216 \):
\[
V = \frac{4}{3} \times 3.14 \times 216
\]
Now, calculating \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]
Now, we can calculate:
\[
V \approx 4.1867 \times 216 \approx 903.8372
\]
Rounding to the nearest hundredth:
\[
V \approx 903.84 \text{ cm}^3
\]
### Volume of Isabella's Snowball
Isabella's snowball has a radius of \( 3 \) cm:
\[
V = \frac{4}{3} \times 3.14 \times (3)^3
\]
Calculating \( (3)^3 = 27 \):
\[
V = \frac{4}{3} \times 3.14 \times 27
\]
Calculating \( \frac{4}{3} \times 3.14 \):
\[
\frac{4}{3} \times 3.14 \approx 4.1867
\]
Now, we can calculate:
\[
V \approx 4.1867 \times 27 \approx 112.99
\]
Rounding to the nearest hundredth:
\[
V \approx 112.99 \text{ cm}^3
\]
### Complete the Statement
Joshua's snowball has a volume of **903.84 cm³**, while Isabella's snowball has a volume of **112.99 cm³**.