Discussion
Three spheres of radii 2cm, 3cm and 6cm are melted to form a new sphere. Find the radius of the new sphere, correct to two decimals.
Answer: A
The radius is 6.31 cm.
The volume of the new sphere equals the sum of the three volumes, so the cubes of the radii add up.
\[ R^{3}=2^{3}+3^{3}+6^{3}=8+27+216=251 \]
\[ R=\sqrt[3]{251}\approx6.31\text{ cm} \]
6.35, 6.55 and 6.15 cm would have cubes of about 256, 281 and 233.
You can check 6.31: its cube is 6.31 × 6.31 × 6.31, about 251.2, which is almost exactly 251. For 6.35 the cube is about 256, for 6.55 about 281 and for 6.15 about 233, which are all too far from 251.
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