1. **Finding Volume of a Cylinder** Problem: Calculate the volume of a cylinder with radius $r$ and height $h$. Formula: $$V = \pi r^2 h$$ Explanation: The volume of a cylinder is the area of the circular base times the height. Example: If $r=3$ and $h=5$, then $$V = \pi \times 3^2 \times 5 = 45\pi$$ cubic units. 2. **Finding Area of a Triangle** Problem: Find the area of a triangle with base $b$ and height $h$. Formula: $$A = \frac{1}{2} b h$$ Explanation: The area is half the product of the base and height. Example: If $b=8$ and $h=6$, then $$A = \frac{1}{2} \times 8 \times 6 = 24$$ square units. 3. **Calculating Percentage Change** Problem: Find the percentage change from an original value $O$ to a new value $N$. Formula: $$\text{Percentage Change} = \frac{N - O}{O} \times 100\%$$ Explanation: Percentage change measures how much a quantity increases or decreases relative to the original. Example: If $O=50$ and $N=65$, then $$\frac{65 - 50}{50} \times 100\% = 30\%$$ increase. 4. **Simplifying Algebraic Fractions** Problem: Simplify the fraction $$\frac{2x^2 + 4x}{2x}$$. Steps: - Factor numerator: $$2x^2 + 4x = 2x(x + 2)$$ - Cancel common factor $2x$: $$\frac{2x(x + 2)}{2x} = x + 2$$ Explanation: Canceling common factors simplifies the fraction. 5. **Basic Statistics - Mean** Problem: Find the mean of the data set: 4, 8, 6, 10. Formula: $$\text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}}$$ Calculation: $$\frac{4 + 8 + 6 + 10}{4} = \frac{28}{4} = 7$$ Explanation: The mean is the average value. These examples cover volume, area, percentage change, algebraic fractions, and statistics.