Question

1. which formula is used to calculate the volume of a sphere?

a. \\( \pi r ^ { 2 } h \\)
b. \\( \frac { 3 } { 4 } \pi r ^ { 2 } \\)
c. \\( 2 \pi r ^ { 3 } \\)
d. \\( \frac { 4 } { 3 } \pi r ^ { 3 } \\)

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: \(\pi r^{2}h\) is the formula for the volume of a cylinder.
• Option b: \(\frac{3}{4}\pi r^{2}\) is not a standard volume formula. The formula for the area of a circle is \(\pi r^{2}\).
• Option c: \(2\pi r^{3}\) is not a standard volume formula.
• Option d: \(\frac{4}{3}\pi r^{3}\) matches the formula for the volume of a sphere.

Answer:

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