Answer:
216 times the original
Step-by-step explanation:
Volume 1 = 4/3 πr³
volume 2 = 4/3 π(6r)³
v 2 / v 1 = 6³ = 216
When the radius of a sphere is multiplied by 6, the volume is multiplied by 216
Let the radius of the sphere be r
The volume of a sphere of radius, r is calculated as:
v = 4/3 πr³
When multiplied by 6, the radius becomes:
R = 6r
The new volume is then calculated as:
V = 4/3 π(6r)³
Divide both volumes
V/v = 4/3 π(6r)³ / 4/3 πr³
Evaluate the quotient
V/v = 6³
V/v = 216
Hence, when the radius of a sphere is multiplied by 6, the volume is multiplied by 216
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