Discussion
The external and internal radii of an empty sphere are 10 cm and 3 cm, respectively. Find the volume of the metal which is required to make it.
Answer: C
The volume is \(4077.\overline{3}\ \text{cm}^{3}\).
The metal is the difference between the outer and inner spheres. Using 22/7 for pi:
\[ V=\frac{4}{3}\cdot\frac{22}{7}\,(10^{3}-3^{3}) \]
\[ V=\frac{88}{21}\times973=4077.\overline{3} \]
The other options differ in the decimal part and do not match.
The shell is hollow, so the metal fills the space between the radius 3 cm and radius 10 cm spheres. The difference of the cubes is 1000 − 27 = 973 and the volume is 4/3 × 22/7 × 973 = 4077.33 cm cubed, which is 4077 with the 3 repeating.
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