Multiple choice

The heights of two metallic right-circular cones are 4.3 cm and 2.1 cm, respectively and the radius of their bases is 1.6 cm each. These two cones are melted together and recast into a sphere. Find the diameter of the sphere.

  1. 3.2 cm

  2. 1.6 cm

  3. 2.56 cm

  4. 5.6 cm

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Volume of two cones = 2 * (1/3 * pi * r^2 * h). Sum = 1/3 * pi * (1.6)^2 * (4.3 + 2.1) = 1/3 * pi * 2.56 * 6.4 = 5.4613 * pi. Sphere volume 4/3 * pi * R^3 = 5.4613 * pi. R^3 = 4.096, so R = 1.6. Diameter = 3.2 cm.

AI explanation

The total volume of the new sphere equals the sum of the volumes of the two cones, using the formula one third pi r squared h. Adding (one third times pi times 1.6 squared times 4.3) and (one third times pi times 1.6 squared times 2.1) gives a total volume of 5.4613 times pi. Equating this to the sphere volume formula (four thirds pi times radius cubed) results in a sphere radius of 1.6 centimeters. The diameter is twice the radius, which is 3.2 centimeters.

Keep practicing — related questions