Grade 8 Ganita Prakash style case-based MCQs

Grade 8 • Case-Based MCQs Exponential Growth

Power Play: Folding Paper & The King’s Diamonds

Two real-life style passages with MCQs testing understanding of doubling, powers, and geometric growth. Includes answers with explanations.

Contents:

• Case Study 1 — The Magical Folding Paper
• Case Study 2 — The King’s Diamonds

Case Study 1 — The Magical Folding Paper

A sheet of paper has an initial thickness of 0.001 cm. When you fold it once, its thickness doubles. This doubling continues with every fold. This is a classic example of exponential growth.

After 10 folds: 1.024 cm (≈ 1 cm)

After 17 folds: ≈ 131 cm (≈ 1.31 m)

After 26 folds: ≈ 670 m

After 30 folds: ≈ 10.7 km (typical airplane altitude)

After 46 folds: > 700,000 km (Earth–Moon scale)

General rule: after n folds, thickness t(n) = 0.001 × 2n cm.

Q1. The thickness after 1 fold is

1. 0.001 cm
2. 0.002 cm
3. 0.01 cm
4. 0.1 cm

Show Answer & Explanation

Answer: (b) 0.002 cm. One fold doubles the thickness.

Q2. After 10 folds, the thickness is about

1. 1 cm
2. 10 cm
3. 100 cm
4. 0.1 cm

Show Answer & Explanation

Answer: (a) 1 cm. Exactly 1.024 cm since 0.001 × 2¹⁰ = 1.024 cm.

Q3. 131 cm (after 17 folds) is closest to

1. length of a pencil
2. height of a chair
3. height of a person
4. height of a door

Show Answer & Explanation

Answer: (c) height of a person (~1.3 m).

Q4. After 26 folds ≈ 670 m. Which is closest?

1. Eiffel Tower (330 m)
2. Burj Khalifa (830 m)
3. Qutub Minar (73 m)
4. Empire State Building (443 m)

Show Answer & Explanation

Answer: (b) Burj Khalifa (830 m) is closest to 670 m among the options.

Q5. 10.7 km (after 30 folds) is comparable to

1. Mariana Trench depth
2. Height at which airplanes fly
3. Height of Mount Everest
4. Depth of a swimming pool

Show Answer & Explanation

Answer: (b) airplane cruising altitude (~10–12 km).

Q6. After 20 folds, thickness is approximately

1. 1 m
2. 10 m
3. 100 m
4. 1 km

Show Answer & Explanation

Answer: (b) 10 m. 0.001 × 220 = 1048.576 cm ≈ 10.49 m.

Q7. The thickness increases after every 3 folds by

1. 2 times
2. 4 times
3. 6 times
4. 8 times

Show Answer & Explanation

Answer: (d) 8 times, since 2³ = 8.

Q8. Exponential growth here means

1. increase by a fixed number
2. double every step
3. decrease every step
4. remain constant

Show Answer & Explanation

Answer: (b) doubles every fold.

Q9. After 46 folds the thickness reaches about 700,000 km. This can reach

1. the Sun
2. the Moon
3. the Mariana Trench
4. Mount Everest

Show Answer & Explanation

Answer: (b) the Moon (Earth–Moon distance scale).

Q10. This growth pattern follows

1. Arithmetic progression
2. Linear growth
3. Geometric progression
4. Subtraction pattern

Show Answer & Explanation

Answer: (c) Geometric progression (common ratio 2).

Case Study 2 — The King’s Diamonds

A king has 3 daughters. Each daughter has 3 baskets. Each basket has 3 keys. Each key opens 3 rooms. Continuing this multiplicative pattern through seven stages gives the total diamonds:

Total diamonds = 3⁷ = 3 × 3 × 3 × 3 × 3 × 3 × 3 = 2187

Computed as 37 = (34) × (33) = 81 × 27 = 2187. Here, 34 corresponds to rooms, and multiplying by 33 accounts for the remaining levels to reach diamonds.

Q1. Total baskets

1. 3
2. 6
3. 9
4. 27

Show Answer & Explanation

Answer: (c) 9, since 3 daughters × 3 baskets each.

Q2. Total keys

1. 9
2. 18
3. 27
4. 81

Show Answer & Explanation

Answer: (c) 27, because 9 baskets × 3 keys each.

Q3. Total rooms

1. 27
2. 34
3. 81
4. 243

Show Answer & Explanation

Answer: (c) 81 = 3⁴ (27 keys × 3 rooms each).

Q4. Total number of diamonds

1. 243
2. 729
3. 2187
4. 6561

Show Answer & Explanation

Answer: (c) 2187. The passage uses seven factors of 3: 3⁷ = 2187.
Note: If you counted only “rooms × 3 diamonds per room,” you’d get 243, but the text clearly frames a 7-stage multiplicative pattern.

Q5. The total diamonds can be expressed as

1. 3⁴
2. 3⁵
3. 3⁶
4. 3⁷

Show Answer & Explanation

Answer: (d) 3⁷. Seven successive “×3” stages.

Q6. If 3⁴ = 81 (rooms), to get 3⁷ you multiply 81 by

1. 3
2. 9
3. 27
4. 243

Show Answer & Explanation

Answer: (c) 27, since 3⁷ = 3⁴ × 3³ = 81 × 27.

Q7. The concept illustrated is

1. Arithmetic progression
2. Powers & exponents
3. Fractions
4. Decimals

Show Answer & Explanation

Answer: (b) Powers & exponents (repeated multiplication by 3).

Teacher Tips

• Estimate vs exact: Have students compute a few exact powers, then use order-of-magnitude comparisons (m, km).
• Structure trees: Draw branching trees for the King’s problem to make exponents countable.
• Discussion prompt: Why does doubling (or multiplying by 3) explode so fast compared to adding?