Case Study Question Mathematics Class 8 on Squares and Cubes

Case Study Question Mathematics Class 8 on Squares and Cubes

Case Study Question Mathematics Class 8 on Squares and Cubes helps students explore perfect squares and cubes using real-life problem-based examples. By solving Case Study math questions for class 9 and math case study questions class 9, learners enhance critical thinking and concept clarity. Moreover, these math case study questions improve calculation speed and build logical reasoning for exam success.

Learning Approach and Practice Benefits

Students practice factorization and estimation to solve Case Study Question Mathematics Class 8 on Squares and Cubes effectively. Additionally, they identify number patterns, connect formulas, and apply them to real scenarios. Therefore, consistent practice strengthens analytical ability and boosts confidence. So, start revising these questions regularly to master square and cube concepts efficiently.

Mathematics Case Study – Swimming Pool Construction

Case Study 5: Construction of a Swimming Pool Using Square and Cube Concepts

A housing society plans to build a square-shaped swimming pool inside a park. The side of the pool will be 25 meters. Around the pool, they plan to make a walkway of uniform width of 2 meters on all sides. The walkway will also be square in shape, surrounding the pool. The management committee needs to find the total area of the walkway and the volume of water that can be filled in the pool if the depth is 2.5 meters. During the calculation, they use the concepts of squares, square roots, cubes, and cube roots to verify measurements and dimensions. Based on the case study, answer the following questions.

1. What is the outer side of the square (including the walkway)?
Solution:
The walkway extends 2 m on each side, so outer side = 25 + 2 + 2 = 29 m.
2. What is the total area of the outer square including the walkway?
Solution:
Area = side² = 29² = 841 m².
3. What is the area of the walkway only?
Solution:
Area of pool = 25² = 625 m². Area of walkway = 841 – 625 = 216 m².
4. What is the volume of water the pool can hold (in m³)?
Solution:
Volume = Area of base × Depth = 625 × 2.5 = 1562.5 m³.
5. If another smaller pool is constructed with one-third the volume of the main pool, what will be its side length (assuming same depth)?
Solution:
Let side of smaller pool = x. Volume of smaller pool = 1/3 × 1562.5 = 520.83 m³. ⇒ x² × 2.5 = 520.83 ⇒ x² = 208.33 ⇒ x = √208.33 ≈ 14.4 m. So the closest side length is 15 m.

Quiz Results

Correct Answers
0
Incorrect Answers
0
Percentage Score
0%

Educational Resources Footer
GitHub