Question

which formula is used to calculate the volume of a sphere?
a. \\( \frac { 3 } { 4 } \pi r ^ { 2 } \\)
b. \\( 2 \pi r ^ { 3 } \\)
c. \\( \frac { 4 } { 3 } \pi r ^ { 3 } \\)
d. \\( \pi r ^ { 2 } h \\)

Explanation:

Step1: Recall the formula for the volume of a sphere

The volume \(V\) of a sphere with radius \(r\) is given by the formula \(V=\frac{4}{3}\pi r^{3}\).

Step2: Analyze each option

• Option a: \(\frac{3}{4}\pi r^{2}\) has the wrong coefficient (\(\frac{3}{4}\) instead of \(\frac{4}{3}\)) and is a 2 - dimensional formula (since the power of \(r\) is 2, it resembles an area formula).
• Option b: \(2\pi r^{3}\) has the wrong coefficient (2 instead of \(\frac{4}{3}\)).
• Option c: \(\frac{4}{3}\pi r^{3}\) matches the formula for the volume of a sphere.
• Option d: \(\pi r^{2}h\) is the formula for the volume of a cylinder (where \(h\) is the height of the cylinder).

Answer:

C. \(\frac{4}{3}\pi r^{3}\)