How many balls,each of radius 2cm can be made from a solid sphere of lead of radius 8cm?
回答 (4)
The radius of the larger ball is 4 times that of the smaller ball (8 cm / 2 cm = 4)
Because length is a one-dimensional measurement and volume is a three-dimensional measurement, the volume of the larger sphere will be 4^3 times as big.
4 x 4 x 4 = 64
So if you melt down the larger sphere you can make 64 of the smaller spheres (assuming no loss of material).
volume = (4/3)πr³
volume of large sphere = (4/3)π(8³) = 2048π/3 cm³
volume of small ball = (4/3)π2³ = 32π/3 cm³
2048π/3 cm³ × (1 ball)/(32π/3 cm³) = 64 balls
Let n be the number of balls with radius 2 cm that can be made.
Total volume of the balls with radius 2 cm = Volume of the sphere with radius 8 cm
n × [(4/3) × π × 2³] = (4/3) × π × 8³
8n = 512
n = 64
Number of balls with radius 2 cm that can be made = 64
收錄日期: 2021-04-18 14:41:30
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