Multiple choice

If the radius of a sphere is increased by $5 \mathrm { cm } ,$ then its surface area increases by 704$\mathrm { cm } ^ { 2 }$ . The radius of the sphere before the increase was:

  1. 2.1 cm

  2. 3.1 cm

  3. 4.1 cm

  4. 5.1 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Surface area S = 4 * pi * r^2. New area = 4 * pi * (r + 5)^2. Increase = 4 * pi * ((r + 5)^2 - r^2) = 704. 4 * (22/7) * (10r + 25) = 704. (10r + 25) = 704 * 7 / 88 = 56. 10r = 31, r = 3.1.

AI explanation

Using the surface area formula for a sphere, 4 pi r squared, the increase in area is 4 pi multiplied by the difference of the squares of the new and old radii. We set 4 pi times ((r plus 5) squared minus r squared) equal to 704. Using pi as 22/7, this simplifies to 10r plus 25 equals 56, which results in a radius of 3.1 cm.

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