Multiple choice

Find the volume and surface area of a sphere of radius $4.2$ cm. $\displaystyle \left [ \pi =\frac{22}{7} \right ]$

  1. $380.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
  2. $320.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
  3. $310.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
  4. $370.46 \,\text{cm}^3,\:221.76 \,\text{cm}^2$
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C Correct answer
Explanation

Volume = (4/3) * pi * r^3 = (4/3) * (22/7) * (4.2)^3 = 310.464. Surface area = 4 * pi * r^2 = 4 * (22/7) * (4.2)^2 = 221.76.

AI explanation

The volume of a sphere is given by the formula four thirds times pi times r cubed, so substituting 4.2 gives four thirds times 22 divided by 7 times 4.2 cubed, resulting in 310.46 cubic cm. The surface area formula is 4 times pi times r squared, which becomes 4 times 22 divided by 7 times 4.2 squared, yielding 221.76 square cm. The correct values are 310.46 cubic cm and 221.76 square cm.

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