Multiple choice

A cone of height 94.5 cm and radius 7 cm was melted. From the melted cone, a sphere was made. Find the radius of the sphere so formed.

  1. 7 cm

  2. 10.5 cm

  3. 13.5 cm

  4. 14 cm

  5. 17.5 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Volume of cone = (1/3) * pi * r^2 * h = (1/3) * pi * 7^2 * 94.5 = pi * 49 * 31.5 = 1543.5 * pi. Volume of sphere = (4/3) * pi * R^3. 1543.5 * pi = (4/3) * pi * R^3. R^3 = 1543.5 * 3 / 4 = 1157.625. R = cube root(1157.625) = 10.5.

AI explanation

Because the cone is melted and recast, the volume of the sphere equals the volume of the cone, giving the equation (4/3)*pi*R^3 = (1/3)*pi*r^2*h. Substituting the cone's height of 94.5 cm and radius of 7 cm yields (4/3)*pi*R^3 = (1/3)*pi*7^2*94.5. Solving for R^3 gives 7^2*94.5/4 = 1157.625, and the cube root of 1157.625 is 10.5 cm.

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