Multiple choice

Volume of a sphere (in cm3) is 13 times its surface area (in cm2). Find the radius of the given sphere.

  1. 36 cm

  2. 39 cm

  3. 42 cm

  4. 44 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

(4/3)pi*r^3 = 13 * (4*pi*r^2). Dividing both sides by 4*pi*r^2 gives r/3 = 13, so r = 39.

AI explanation

The volume of a sphere is given by (4/3) * pi * r^3 and its surface area is 4 * pi * r^2. Setting the volume equal to 13 times the surface area results in the equation (4/3) * pi * r^3 = 13 * 4 * pi * r^2. Dividing both sides by 4 * pi * r^2 leaves r / 3 = 13, which gives a radius of r = 39 cm. The radius of the given sphere is 39 cm.

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