Multiple choice

Two right circular cones of dimensions h=4.1, r=2.1 cm and h = 4.3 cm, r = 2.1 cm are melted to form a sphere of radius

  1. 2.5 cm

  2. 2.7 cm

  3. 2.1 cm

  4. 2 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Volume of cone = 1/3 * pi * r^2 * h. V1 = 1/3 * pi * 2.1^2 * 4.1. V2 = 1/3 * pi * 2.1^2 * 4.3. Total V = 1/3 * pi * 2.1^2 * (4.1 + 4.3) = 1/3 * pi * 2.1^2 * 8.4. Sphere volume = 4/3 * pi * R^3. 4/3 * pi * R^3 = 1/3 * pi * 2.1^2 * 8.4. 4R^3 = 2.1^2 * 8.4. R^3 = 2.1^2 * 2.1 = 2.1^3. R = 2.1.

AI explanation

By equating the total volume of the two cones to the volume of the new sphere, we use the formulas for cone and sphere volumes. The sum of the cone volumes is one third multiplied by pi multiplied by 2.1 squared multiplied by the sum of the heights 4.1 and 4.3. This equals four thirds multiplied by pi multiplied by the new radius cubed, so the radius cubed equals one quarter of 2.1 squared multiplied by 8.4, which results in exactly 9.261. Taking the cube root of 9.261 gives a sphere radius of 2.1 cm.

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