Multiple choice

A sphere of radius 16 cm is melted and recast into a number of smaller spheres, each of radius 2 cm. Find the number of smaller spheres made.

  1. 64

  2. 27

  3. 8

  4. 512
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Volume of large sphere = (4/3) * pi * 16^3. Volume of small sphere = (4/3) * pi * 2^3. Number of spheres = (16/2)^3 = 8^3 = 512.

AI explanation

Since the volume remains constant when the large sphere is recast, the number of smaller spheres is the volume of the large sphere divided by the volume of one small sphere. Using the sphere volume formula, this becomes ((4/3)pi(16)^3) divided by ((4/3)pi(2)^3). The ratio simplifies to 8 cubed, which equals 512 smaller spheres.

Keep practicing — related questions