Answer:
24 centimeters
Step-by-step explanation:
A basketball is a sphere. The volume of a sphere can be found using the following formula:
V= 4/3 π r^3
We know that the volume is 2304 π cm^3, therefore we can substitute 2304π in for V.
2304π = 4/3 π r^3
We want to find out what r is. Therefore, we must get r by itself. First, divide both sides by pi.
2304π/π=4/3πr^3/π
2304π/π=4/3r^3
2304=4/3r^3
Next, divide both sides by 4/3, or multiply by the reciprocal of 4/3. The reciprocal of 4/3 is 3/4 (flip the numerator and denominator).
2304*3/4=4/3r^3*3/4
2304*3/4=r^3
1728=r^3
Now, take the cube root of both sides.
∛1728=∛r^3
∛1728=r
12=r
r= 12 cm
The radius is 12 centimeters, but the question asks us to find the diameter. The diameter is twice the radius.
d= 2r
d= 2* 12 cm
d= 24 cm
The diameter of the basketball is 24 centimeters.
