Perfect Squares and Cubes – Math Case Study Question for Class 8

Perfect Squares and Cubes – Math Case Study Question for Class 8

Perfect Squares and Cubes – Math Case Study Question for Class 8 helps students identify number patterns, perfect squares, and cube relationships through logical exercises. These activities also relate to Case Study math questions for class 9 and math case study questions class 9, enhancing conceptual clarity. Moreover, solving math case study questions improves accuracy, reasoning, and strengthens fundamental mathematical skills.

Concept Understanding and Practice Benefits

Students gain confidence in solving Perfect Squares and Cubes – Math Case Study Question for Class 8 using factorization and estimation. Additionally, they build a strong foundation for algebraic learning. Therefore, these exercises prepare learners for higher classes effectively. So, with regular practice and conceptual revision, students can excel in both exams and real-life problem-solving.

Mathematics Case Study – Squares and Square Roots

Case Study 3: Solar Panel Installation and Estimation Using Squares and Square Roots

An environment club in a school decided to install solar panels on the terrace to generate electricity for their classrooms. The terrace is a perfect square with each side measuring 20 meters. Each solar panel is square-shaped with a side of 2 meters. The students need to calculate how many panels can fit on the terrace without overlapping and how much area each panel covers. They also plan to install a small square water tank for cleaning the panels, whose base area is 16 m². The club members decided to calculate the side of the tank’s base using the concept of square roots. These calculations help them understand how mathematical concepts of squares and square roots are useful in real-life situations such as design, construction, and environmental planning.

1. What is the total area of the terrace?
Solution:
Area of terrace = side² = 20² = 400 m².
2. What is the area of one solar panel?
Solution:
Area = 2² = 4 m².
3. How many such panels can be placed on the terrace?
Solution:
Total panels = Total area / Area of one panel = 400 / 4 = 100.
4. The base area of the water tank is 16 m². What is the length of one side of its base?
Solution:
Side = √16 = 4 m.
5. If the terrace area is increased such that each side becomes 1.5 times longer, what will be the new area?
Solution:
New side = 1.5 × 20 = 30 m. New area = 30² = 900 m².

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