Correct option is C
Given:
· Total surface area of big sphere = 5544 cm²
· Diameter of each small ball = 0.5 cm
· Radius of each ball = 0.25 cm
We need to find: How many tiny balls can be made from the
volume of the big sphere.
Formula:
1. Surface area of sphere = 4πR²
2. Volume of sphere = (4/3)πr³
3. Number of balls = Volume of big sphere ÷ Volume of one small ball
Solution:
Step 1: Find radius of big sphere
4πR² = 5544
Take π = 22/7:
4 × (22/7) × R² = 5544 ⇒ R² = (5544 × 7) ÷ 88 ⇒ R² = 441 ⇒ R = 21 cm
Step 2: Volume of big sphere
Volume = (4/3)πR³ = (4/3) × (22/7) × (21³) = 38808 cm³
Step 3: Volume of small ball
r = 0.25 cm
Volume = (4/3)π(0.25³) = (4/3) × (22/7) × 0.015625 = 0.065476 cm³
Step 4: Number of balls
= 38808 ÷ 0.065476 =
74,088
Correct Answer: (c) 74,088
