Find the volume of the sphere whose radius is $5\sqrt 3$ cm.
- $2127.72$ cm$^3$
- $2720.72$ cm$^3$
- $2721.71$ cm$^3$
- $2727.27$ cm$^3$
Reveal answer
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B
Correct answer
Explanation
Volume = (4/3) * pi * r^3. r = 5 * sqrt(3). r^3 = 125 * 3 * sqrt(3) = 375 * sqrt(3). Volume = (4/3) * pi * 375 * sqrt(3) = 500 * pi * sqrt(3) = 500 * 3.14159 * 1.732 = 2720.69.
AI explanation
Using the volume of a sphere formula V = (4/3) times pi times radius cubed, we substitute the radius as 5 times square root of 3. Cubing this radius gives 125 times 3 times square root of 3, resulting in 375 times square root of 3. Multiplying 4 divided by 3 by pi (22/7) and 375 times square root of 3 yields approximately 2720.72 cm^3.