The volume V of a sphere can be expressed in terms of its radius r according to the function V(r) = 4 3 𝜋r3. Find the volume of a basketball if the diameter of the ball is 29.5 centimeters.

Answer 1

To solve this question, we must first divide the diameter by 2 to get a radius of 14.75. We then plug our value of 14.75cm into the equation V = (4/3)(π)(r³) like so:

V = (4/3) * (π) * (14.75 cm)³

Using PEMDAS, we first check for any operations inside parentheses. After seeing that there is nothing for us to do for P, we then move on to the exponent. When we plug 29.5³ into a calculator, we find that after rounding to the nearest whole number we get the answer 3,209 cubic cm (cm³). Plugging that into our equation now, we find that it is:

V = (4/3) * (π) * (3,209 cm³)

We then use the M in PEMDAS, which stands for multiplication, to multiply out our terms. In doing this along with again rounding, we find that we get:

V = 4,279 * π cm³

We can simplify this even further by multiplying this number by the numerical value of pi, 3.1415. Doing this gives us:

V =13,442 cm³

Funnily enough, 1 cm³ is equal to 1 milliliter (mL), so you could also express this value as 13,442 mL. If we wanted to go even further, we could say that we know that 1000 mL is equal to 1 liter (L), so we could make our answer look even prettier by dividing it by 1000 and calling it 13.4 L.