Surface Areas and Volumes Class 10 Case Study

Surface Areas and Volumes Class 10 Case Study

Surface Areas and Volumes Class 10 Case Study | CBSE & NCERT Questions

Surface Areas and Volumes Class 10 Case Study

In CBSE mathematics, Surface Areas and Volumes Class 10 Case Study questions are essential for exam success. Students practice Case Study Questions on Mensuration and solve Mensuration Case Study Questions Class 10 to strengthen real-world applications of cylinders, cones, and spheres. These problems encourage logical thinking and practical learning.

Practice With Case Study PDFs

Many resources offer Class 10 Maths case study for self-study. These collections include Cbse Class 10 Case Study math case study along with detailed case study on menuration . Students can also refer to Class 10 Maths Case Study for systematic revision.

Exam-Focused Preparation

For board preparation, math case studies play a key role. Moreover, Case Study on mensuration ensures clarity of concepts. Practicing Class 10 Case Study Questions Maths Surface Areas and Volumes regularly, along with Cbse Case Study Questions Maths Class 10 Surface Areas and Volumes, boosts confidence and accuracy. Therefore, consistent practice leads to better results in exams.

Case Study 1: Fuel Tanks Manufacturing

Case Study 1

A company manufactures long transportable fuel tanks shaped as a capsule: a right circular cylinder of length 6.0 meters capped at both ends by hemispheres of radius 1.5 meters. These tanks will be painted on the entire outer curved surface (including both hemispherical ends) with an anti-corrosive coat. The engineering team needs accurate calculations for material ordering, painting cost estimates and capacity planning. Each tank will be filled with diesel and transported to remote depots. For safety checks they also want to know the usable volume in cubic meters and in liters, and how many such tanks are needed to store a specified batch of 200,000 liters. Use π = 22/7 for all calculations. Based on this scenario answer the following questions. (Note: 1 cubic meter = 1000 liters.)

1. The total outer curved surface area (cylinder curved surface plus both hemispherical outer surfaces) of one tank is (in square meters):

Answer: (a) 84.86 m²

Solution: Radius r = 1.5 m, cylinder length h = 6.0 m. Curved surface area of cylinder = 2πrh = 2 × (22/7) × 1.5 × 6 = 396/7 m² ≈ 56.5714 m². Combined outer area of two hemispheres = 4πr² = 4 × (22/7) × (1.5)² = 198/7 m² ≈ 28.2857 m². Total outer curved surface area = (396+198)/7 = 594/7 m² ≈ 84.8571 m² ≈ 84.86 m². Option (a) matches.

2. The internal volume (capacity) of one tank in cubic meters is:

Answer: (a) 56.57 m³

Solution: Volume of cylinder = πr²h = (22/7) × (1.5)² × 6 = 297/7 m³ ≈ 42.4286 m³. Volume of two hemispheres = (4/3)πr³ = (4/3) × (22/7) × (1.5)³ = 297/21 m³ ≈ 14.1429 m³. Total volume = 297/7 + 297/21 = 1188/21 = 594/7 m³ ≈ 56.5714 m³. Option (a) matches.

3. The capacity of one tank in liters (rounded to nearest liter) is:

Answer: (a) 56,571 L

Solution: 56.5714 m³ × 1000 = 56,571.4 L. Rounded = 56,571 L. Option (a) matches.

4. If painting is charged at Rs. 35 per square meter for the entire outer curved surface, the painting cost for one tank (rounded to nearest rupee) is:

Answer: (a) Rs. 2970

Solution: Total outer area = 594/7 m². Cost = (594/7) × 35 = 594 × 5 = 2970 Rs. Option (a) matches exactly.

5. How many such tanks are required to store a batch of 200,000 liters of diesel? (Assume whole tanks only)

Answer: (a) 4

Solution: Capacity per tank = 56,571.4 L. Number required = 200,000 / 56,571.4 ≈ 3.535. Since only whole tanks can be used, take next whole number = 4. Option (a) matches.

Quiz Results

Correct Answers: 0

Incorrect Answers: 0

Percentage Score: 0%

Educational Resources Footer

Free Educational Resources

Free Study Material English Vocabulary Tests Grammar for Hearing Impaired Math for Hearing Impaired English Vocabulary Case Study Questions Math GRE Vocabulary Tests LaTeX Tutorial R Programming Tests Online English Games Online Math Games Learn Computer Basics JEE Math Tests CAT Quant Tests Increase Calculation Speed Class 10 Math Tests Prompt Engineering SAT Math Tutorial Logic Quizzes Grade 1 Logic Quizzes Grade 2

© 2023 Udgam Welfare Foundation. All rights reserved.