The formula for the volume of a cone is [tex]$V=\frac{1}{3} b h$[/tex]. Solve [tex]$V=\frac{1}{3} b h$[/tex] for [tex]$b$[/tex], the base of the cone.
A. [tex]$b=\frac{h}{3 V}$[/tex]
B. [tex]$b=\frac{V}{3 h}$[/tex]
C. [tex]$b=\frac{3 h}{V}$[/tex]
D. [tex]$b=\frac{3 V}{h}$[/tex]
Answer (1)
Multiply both sides of the equation by 3: 3 V = bh .
Divide both sides of the equation by h : b = h 3 V .
The base of the cone is: b = h 3 V .
Explanation
Understanding the Formula We are given the formula for the volume of a cone: V = 3 1 bh , where V is the volume, b is the base, and h is the height. Our goal is to isolate b on one side of the equation.
Multiplying by 3 To isolate b , we first multiply both sides of the equation by 3: 3 × V = 3 × 3 1 bh 3 V = bh
Dividing by h Next, we divide both sides of the equation by h :
h 3 V = h bh h 3 V = b
The Solution Thus, we have solved for b :
b = h 3 V
Examples
Understanding how to rearrange formulas like the volume of a cone is useful in many real-world situations. For example, if you know the volume and height of a cone-shaped pile of sand, you can determine the area of the base it covers. This is also applicable in architecture when designing conical structures, ensuring you have the correct base dimensions for a given volume and height. This skill is fundamental in various fields requiring geometric calculations.
