Multiple choice

The volume of a sphere is $\dfrac {88}{21}\times (14)^{3} cm^{3}$. The curved surface of the sphere is (Take $\pi = \dfrac {22}{7}$).

  1. $2424\ cm^{2}$
  2. $2446\ cm^{2}$
  3. $2484\ cm^{2}$
  4. $2464\ cm^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume = 4/3 * pi * r^3 = 88/21 * 14^3. 4/3 * 22/7 * r^3 = 88/21 * 14^3. 88/21 * r^3 = 88/21 * 14^3. So r = 14. Surface area = 4 * pi * r^2 = 4 * 22/7 * 14 * 14 = 4 * 22 * 2 * 14 = 2464.

AI explanation

The volume of a sphere is (4/3) * pi * r^3, which is given as (88/21) * 14^3. Equating the two gives (4/3) * (22/7) * r^3 = (88/21) * 14^3, meaning r^3 = 14^3 and the radius r is 14 cm. The curved surface area of a sphere is 4 * pi * r^2, so substituting the radius gives 4 * (22/7) * 14^2. This calculates to 4 * 22 * 28 = 2464 sq cm.

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