JAMB 2022 Mathematics · Question 9

Given that r = $\sqrt \frac{3v}{\pi h}$ , make v the subject of the formula

Options

A.v = 3 $πr^2$ h
B.v = $\frac{πrh}{3}$
C.v = $\frac{πr^2h}{3}$
D.v = 3πrh

Answer: C. v = $\frac{πr^2h}{3}$

Explanation written with AI and checked against the answer key

To make $v$ the subject of the formula, we need to isolate it on one side of the equation. Let's break this down step-by-step.

1. Analyze the equation

We are given:

r = \sqrt{\frac{3v}{\pi h}}

Our goal is to get $v$ by itself.

2. Explain the concept

To solve for a variable trapped inside a square root, we must perform the inverse operation, which is squaring both sides. Once the square root is removed, we can use basic algebraic manipulation (multiplication and division) to isolate $v$ .

3. Step-by-step solution

Step 1: Square both sides to remove the square root.

r^2 = \left( \sqrt{\frac{3v}{\pi h}} \right)^2

r^2 = \frac{3v}{\pi h}

Step 2: Clear the fraction by multiplying both sides by $(\pi h)$ .

r^2 \times (\pi h) = 3v

\pi r^2 h = 3v

Step 3: Isolate $v$ by dividing both sides by 3.

\frac{\pi r^2 h}{3} = v

Rearranging it to look like the standard form:

v = \frac{\pi r^2 h}{3}

4. Identify the answer

Comparing our result to the given options: A. $v = 3\pi r^2 h$ B. $v = \frac{\pi rh}{3}$ C. $v = \frac{\pi r^2 h}{3}$ D. $v = 3\pi rh$

The correct option is C.

5. Exam Tip

When dealing with "change of subject" questions involving square roots, always square both sides first to "free" the variables inside. If you have a fraction, multiply to clear the denominator immediately after squaring. This prevents common errors like forgetting to square the other side of the equation!

AI can make mistakes. Report anything that looks wrong.

Given that r = 3vπ h \sqrt \frac{3v}{\pi h} ​π h3v​, make v the subject of the formula