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Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. What is the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm?
- a)120
- b)130
- c)150
- d)180
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of di...
Let the no. of marbles = x
Radius of marble = 1.4/2 = 0.7 cm
Radius of cylinder = 7/2 = 3.5 cm
⇒ x = 150
Radius of marble = 1.4/2 = 0.7 cm
Radius of cylinder = 7/2 = 3.5 cm
⇒ x = 150
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Community Answer
Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of di...
Given data:
Diameter of marbles = 1.4 cm
Diameter of beaker = 7 cm
Water level rises by = 5.6 cm
Calculating volume of water displaced by one marble:
Radius of marble = Diameter/2 = 1.4/2 = 0.7 cm
Volume of a sphere = (4/3) * π * r^3
Volume of one marble = (4/3) * 3.14 * 0.7^3 = 1.436 cm^3
Calculating volume of water displaced by 'n' marbles:
Let the number of marbles be 'n'
Total volume of water displaced = Volume of one marble * n
5.6 * π * (3.5)^2 = 1.436 * n
n = (5.6 * 3.14 * 3.5 * 3.5) / 1.436
n ≈ 150
Therefore, the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm is approximately 150. Hence, the correct answer is option 'C'.
Diameter of marbles = 1.4 cm
Diameter of beaker = 7 cm
Water level rises by = 5.6 cm
Calculating volume of water displaced by one marble:
Radius of marble = Diameter/2 = 1.4/2 = 0.7 cm
Volume of a sphere = (4/3) * π * r^3
Volume of one marble = (4/3) * 3.14 * 0.7^3 = 1.436 cm^3
Calculating volume of water displaced by 'n' marbles:
Let the number of marbles be 'n'
Total volume of water displaced = Volume of one marble * n
5.6 * π * (3.5)^2 = 1.436 * n
n = (5.6 * 3.14 * 3.5 * 3.5) / 1.436
n ≈ 150
Therefore, the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm is approximately 150. Hence, the correct answer is option 'C'.
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Marbles of diameter 1.4 cm are dropped into a cylindrical beaker of diameter 7 cm containing some water. What is the number of marbles that should be dropped into the beaker so that the water level rises by 5.6 cm?a)120b)130c)150d)180Correct answer is option 'C'. Can you explain this answer?
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