Given that \( V=\frac{1}{3} \pi r^{2} h \), a) Make \( r \) the subject of the formula b) Find \( r \) given that \( h=9 \mathrm{~cm} \) and \( V=1848 \mathrm{~cm}^{3} \) and \( \pi=\frac{22}{7} \).

Let's solve the problem step by step. ### a) Making \( r \) the Subject of the Formula Given the volume formula of a cone: \[ V = \frac{1}{3} \pi r^{2} h \] To solve for \( r \), follow these steps: 1. **Multiply both sides by 3** to eliminate the fraction: \[ 3V = \pi r^{2} h \] 2. **Divide both sides by \( \pi h \)** to isolate \( r^2 \): \[ r^{2} = \frac{3V}{\pi h} \] 3. **Take the square root of both sides** to solve for \( r \): \[ r = \sqrt{\frac{3V}{\pi h}} \] **Final Formula:** \[ r = \sqrt{\frac{3V}{\pi h}} \] ### b) Finding \( r \) Given \( h = 9 \, \text{cm} \), \( V = 1848 \, \text{cm}^3 \), and \( \pi = \frac{22}{7} \) Using the formula derived in part (a): \[ r = \sqrt{\frac{3V}{\pi h}} \] Plug in the given values: \[ r = \sqrt{\frac{3 \times 1848}{\frac{22}{7} \times 9}} \] **Step-by-Step Calculation:** 1. **Calculate the numerator:** \[ 3 \times 1848 = 5544 \] 2. **Calculate the denominator:** \[ \frac{22}{7} \times 9 = \frac{198}{7} \] 3. **Form the fraction inside the square root:** \[ \frac{5544}{\frac{198}{7}} = \frac{5544 \times 7}{198} = \frac{38808}{198} \] 4. **Simplify the fraction:** \[ \frac{38808}{198} = 196 \] (Since \( 198 \times 196 = 38808 \)) 5. **Take the square root:** \[ r = \sqrt{196} = 14 \, \text{cm} \] **Final Answer:** \[ r = 14 \, \text{cm} \]