To calculate the volume of a sphere, we use the formula:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
where [tex]\( V \)[/tex] is the volume, [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.141592653589793, and [tex]\( r \)[/tex] is the radius of the sphere.
Given that the radius [tex]\( r \)[/tex] is 7 cm, we can substitute this value into the formula:
[tex]\[ V = \frac{4}{3} \pi (7)^3 \][/tex]
First, calculate [tex]\( (7)^3 \)[/tex]:
[tex]\[ 7^3 = 7 \times 7 \times 7 = 343 \][/tex]
Next, multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ \pi \times 343 = 3.141592653589793 \times 343 \approx 1079.1380344384983 \][/tex]
Now, multiply this result by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[ \frac{4}{3} \times 1079.1380344384983 \approx 1436.7550402417319 \][/tex]
Thus, the exact volume of the sphere is approximately [tex]\( 1436.7550402417319 \)[/tex] cubic centimeters.
To give the answer to 1 decimal place, we round this value:
[tex]\[ 1436.7550402417319 \approx 1436.8 \][/tex]
Thus, the volume of the sphere is [tex]\( 1436.8 \)[/tex] cubic centimeters (cm[tex]\(^3\)[/tex]), rounded to one decimal place.
