Question

the formula for the volume of a sphere is:
o a. (\frac{4}{3}pi r^{3})
o b. (\frac{1}{2}pi r^{2}h)
o c. (pi d^{2}h)
o d. (pi r^{2}h)
when calculating the volume of a sphere, you need to use which
mathematical constant?
o a. i
o b. e
o c. (pi)
o d. (\theta)

Explanation:

• For the formula of the volume of a sphere, the standard formula is \(V = \frac{4}{3}\pi r^{3}\). Among the given options, option a (\(\frac{4}{3}\pi r^{3}\)) is the correct formula. Options b (\(\frac{1}{2}\pi r^{2}h\)) is not a standard volume formula for a sphere. Option c (\(\pi d^{2}h\)) and option d (\(\pi r^{2}h\)) are formulas related to cylinder - like (for option d, volume of a cylinder \(V=\pi r^{2}h\)) or incorrect manipulations for a sphere.
• When calculating the volume of a sphere (\(V=\frac{4}{3}\pi r^{3}\)), the mathematical constant \(\pi\) (pi) is used. The constant \(i\) is the imaginary unit (\(i=\sqrt{- 1}\)), \(e\approx2.718\) is the base of the natural logarithm, and \(\theta\) is often used to represent an angle.

Answer:

a. \(\frac{4}{3}\pi r^{3}\) (for the volume formula of a sphere) and c. \(\pi\) (for the mathematical constant).