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A solid metallic cone of height 10 cm and radius of base 20 cm is melted to make spherical balls each of 4 cm diameter. How many such balls can be made?
- a)25
- b)50
- c)125
- d)75
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
A solid metallic cone of height 10 cm and radius of base 20 cm is mel...
Volume of cone = 1/3πr2h
=(1/3)×π×(20)2×10
=400×10
=(π/3)×4000=(4000/3)π
The volume of spherical balls = 4/3πr3
=(4/3)×π×(2)2
= 32/3π
∴ Spherical balls are formed from the cones.
∴ The total volume of all spherical cones = Volume of cones.
∴ No. of spherical balls = Volume of cone/Vol of 1 spherical ball
=4000/3
=32/3
=4000/32=125
Most Upvoted Answer
A solid metallic cone of height 10 cm and radius of base 20 cm is mel...
Given Data:
- Height of cone = 10 cm
- Radius of cone's base = 20 cm
- Diameter of spherical balls = 4 cm
Calculations:
- Volume of cone = 1/3 * π * r^2 * h, where r is the radius and h is the height of the cone
- Volume of cone = 1/3 * π * 20^2 * 10
- Volume of cone = 1/3 * π * 400 * 10
- Volume of cone = 4000π cm^3
- Volume of one spherical ball = (4/3) * π * (2)^3, where 2 is the radius of the ball (half of the diameter)
- Volume of one spherical ball = (4/3) * π * 8
- Volume of one spherical ball = 32π cm^3
- Number of balls that can be made = Volume of cone / Volume of one spherical ball
- Number of balls = 4000π / 32π
- Number of balls = 125
Therefore, 125 spherical balls of 4 cm diameter can be made from the given metallic cone. Hence, the correct answer is option 'C) 125'.
- Height of cone = 10 cm
- Radius of cone's base = 20 cm
- Diameter of spherical balls = 4 cm
Calculations:
- Volume of cone = 1/3 * π * r^2 * h, where r is the radius and h is the height of the cone
- Volume of cone = 1/3 * π * 20^2 * 10
- Volume of cone = 1/3 * π * 400 * 10
- Volume of cone = 4000π cm^3
- Volume of one spherical ball = (4/3) * π * (2)^3, where 2 is the radius of the ball (half of the diameter)
- Volume of one spherical ball = (4/3) * π * 8
- Volume of one spherical ball = 32π cm^3
- Number of balls that can be made = Volume of cone / Volume of one spherical ball
- Number of balls = 4000π / 32π
- Number of balls = 125
Therefore, 125 spherical balls of 4 cm diameter can be made from the given metallic cone. Hence, the correct answer is option 'C) 125'.
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A solid metallic cone of height 10 cm and radius of base 20 cm is melted to make spherical balls each of 4 cm diameter. How many such balls can be made?a)25b)50c)125d)75Correct answer is option 'C'. Can you explain this answer?
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