Case Study Question 1: Area of a Rectangle
In a school garden, the principal wants to create a rectangular flower bed. The length of the flower bed is 8 meters, and the width is 5 meters.
Question: Calculate the area of the flower bed and determine how much soil is needed to fill it.
Answer:
- Formula for Area: Area = Length × Width
- Calculation:
- Length = 8 m
- Width = 5 m
- Area = 8 m × 5 m = 40 m²
- Conclusion: The area of the flower bed is 40 square meters. Therefore, 40 cubic meters of soil will be needed to fill the flower bed.
Case Study Question 2: Ratio in a Classroom
In a class of 30 students, the ratio of boys to girls is 2:3.
Question: Find the number of boys and girls in the class.
Answer:
- Understanding Ratios: The ratio of boys to girls is 2:3, which means for every 5 students, 2 are boys and 3 are girls.
- Total Parts: 2 + 3 = 5 parts
- Value of One Part:
- Total Students = 30
- Value of One Part = Total Students / Total Parts = 30 / 5 = 6
- Number of Boys and Girls:
- Boys = 2 parts × 6 = 12
- Girls = 3 parts × 6 = 18
- Conclusion: There are 12 boys and 18 girls in the class.
Case Study Question 3: Simple Interest
A student invests 2000 INR in a bank saving account at an interest rate of 5% per annum for 3 years.
Question: Calculate the simple interest earned.
Answer:
- Formula for Simple Interest: Simple Interest = Principal × Rate × Time / 100
- Calculation:
- Principal = 2000 INR
- Rate = 5%
- Time = 3 years
- Simple Interest = 2000 × 5 × 3 / 100 = 300 INR
- Conclusion: The simple interest earned after 3 years is 300 INR.