Question

question 23 of 50
what is the formula for the volume of a sphere with r = a?
○ $v = \frac{4}{3}\pi a^3$
○ $v = \frac{1}{3}\pi a^2 h$
○ $v = \pi a^2 h$
○ $v = 4\pi a^2$
○ $v = \frac{1}{3}bh$

Explanation:

Step1: Recall Sphere Volume Formula

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

Step2: Substitute \( r = a \)

Given \( r = a \), substitute \( r \) with \( a \) in the formula. So the formula becomes \( V=\frac{4}{3}\pi a^{3} \).

Step3: Match with Options

Check the options:

• First option: \( V = \frac{4}{3}\pi a^{3} \) (matches the derived formula).
• Second option: \( V=\frac{1}{3}\pi a^{2}h \) is the volume of a cone.
• Third option: \( V = \pi a^{2}h \) is the volume of a cylinder.
• Fourth option: \( V = 4\pi a^{2} \) is the surface area of a sphere.
• Fifth option: \( V=\frac{1}{3}Bh \) is the volume of a pyramid.

Answer:

A. \( V = \frac{4}{3}\pi a^{3} \)