Mathematics
24.09.2021 21:04
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Asolid metal sphere of radius 32cm is melted down and recast to make 64 identical

Asolid metal sphere of radius 32cm is melted down and recast to make 64 identical small spheres.what will be the radius of each small sphere?
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ameera1973
ameera1973
5,0(7 marks)
V_1=\frac{4}{3}\pi R^3\\\\R=32cm\\\\V_1=\frac{4}{3}\pi\cdot32^3=\frac{131072}{3}\pi\ (cm^3)\\\\V_2=V_1:64\\\\V_2=\frac{131072}{64}\pi:64=\frac{131072}{3}\pi\cdot\frac{1}{64}=\frac{2048}{3}\pi\ (cm^3)\\\\r=?\\\\V_2=\frac{4}{3}\pi r^3

\frac{4}{3}\pi r^3=\frac{2048}{3}\pi\ \ \ /:\pi\\\\\frac{4}{3}r^3=\frac{2048}{3}\ \ \ /\cdot\frac{3}{4}\\\\r^3=512\\\\r=\sqrt[3]{512}\\\\r=8\ (cm)\leftarrow answer
rivermadds1514
rivermadds1514
4,7(6 marks)

All numbers divisible by 9 are also divisible by 3.

Step-by-step explanation:

Nine is basically just 3 3's.

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