The premise of this question contains a mistake in the unit for the volume of the orange—it should be in cubic centimeters (cm³), not square centimeters (cm²). Volume is a measure of three-dimensional space, while square centimeters measure area, which is two-dimensional. Assuming that the volume of the orange is indeed 288 cubic centimeters (288 cm³), we can calculate the radius of the fruit by considering it as a perfect sphere.
The formula for the volume of a sphere is:
V = (4/3)πr³
where V is the volume, r is the radius, and π (pi) is a mathematical constant approximately equal to 3.14159.
Given the volume V = 288 cm³, we need to solve the formula for r (the radius):
288 = (4/3)πr³
First, we multiply both sides of the equation by 3/(4π) to isolate r³ on one side:
3/(4π) * 288 = r³
Next, we find the numerical value of 3/(4π):
3/(4π) ≈ 0.23873241463
Now multiply this value by the volume:
0.23873241463 * 288 = r³
r³ ≈ 68.7950346
To find the value of r, we take the cube root of r³:
r ≈ ³√68.7950346
Using a calculator, we find:
r ≈ 4.12 cm
So, the radius of the orange is approximately 4.12 centimeters.
