Mensuration Class 8 Case Study Questions and Answers

Mensuration Class 8 Case Study Questions and Answers (CBSE PDF)

Chapter: Mensuration Class 8 Case Study Questions and Answers

Mensuration Class 8 Case Study Questions and Answers help students understand concepts through real-life applications. These questions include diagrams, structured explanations, and clear solutions. Moreover, they follow the CBSE competency-based pattern to support effective preparation. Students can use them for revision and concept reinforcement.

Key Topics Included

The material covers perimeter, area, surface area, and volume with practical scenarios. Additionally, each case study encourages analytical thinking. This approach builds strong problem-solving skills and improves accuracy in exams.

Benefits for Class 8 Learners

These case studies enhance understanding through step-by-step reasoning. Furthermore, they are simple to revise and easy to practice. As a result, students gain confidence and perform better in assessments.

Mensuration Class 8 Case Study Questions and Answers (CBSE PDF)

The school is organising an annual fair and prepares several structures on the playground. A **rectangular banner** ($12$ m length, $7$ m width) is fixed above the main gate. A rainwater collection system uses a **cylindrical tank** (radius $2$ m, height $6$ m) topped with a **hemispherical dome** (same radius). Small **cuboidal stalls** ($4$ m $\times 3$ m $\times 2.5$ m) are built for selling, and one stall is covered by a **conical roof** (radius $3$ m, height $4$ m). The organising team needs to calculate areas and volumes (banner cloth, stall paint, tank capacity, and roof material) to manage the budget.

1. What is the area of the rectangular banner above the gate?

Solution:
Area of rectangle $A = \text{length} \times \text{width} = 12 \times 7 = 84$ sq m.
Correct answer is option **(b)**.

2. What is the total volume of the rainwater tank (cylinder + hemispherical dome)? Express your answer in terms of $\pi$.

Solution:
Volume of cylinder $V_{cyl} = \pi r^{2}h = \pi \times 2^{2}\times 6 = 24\pi$.
Volume of hemisphere $V_{hemi} = \frac{2}{3}\pi r^{3} = \frac{2}{3}\pi \times 2^{3} = \frac{16}{3}\pi$.
Total volume $= V_{cyl} + V_{hemi} = 24\pi + \frac{16}{3}\pi$ cubic m.
Correct answer is option **(b)**.

3. What is the total surface area (TSA) to be painted for the cuboidal stall ($l=4$m, $w=3$m, $h=2.5$m)?

Solution:
TSA of cuboid $TSA = 2(lw + lh + wh)$
$TSA = 2((4 \times 3) + (4 \times 2.5) + (3 \times 2.5))$
$TSA = 2(12 + 10 + 7.5) = 2 \times 29.5 = 59$ sq m.
Correct answer is option **(b)**.

4. What is the lateral (curved) surface area (LSA) of the conical roof (radius $r=3$m, height $h=4$m)?

Solution:
First, find the slant height $l$: $l=\sqrt{r^{2}+h^{2}}=\sqrt{3^{2}+4^{2}}=\sqrt{25}=5$ m.
LSA of cone $LSA = \pi r l = \pi \times 3 \times 5 = 15\pi$ sq m.
Correct answer is option **(b)**.

5. Which mensuration measure is needed to find how much soil is required to fill a rectangular planter ($2$m $\times 1$m $\times 0.5$m)?

Solution:
The amount of material that fills a 3D space is measured by **Volume**.
Correct answer is option **(d)**.

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