Multiple choice

The total surface area of a solid cube is 4.86 m2. It is melted and recast into a right circular cylinder of radius 0.3 m. What is the height (in m) of the cylinder (correct to one decimal place)? Take π = 22/7.

  1. 2.6

  2. 2.8

  3. 1.8

  4. 3.5
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Surface area of cube = 6a^2 = 4.86, so a^2 = 0.81, a = 0.9. Volume of cube = a^3 = 0.729. Volume of cylinder = pi * r^2 * h = (22/7) * (0.3)^2 * h = 0.729. h = (0.729 * 7) / (22 * 0.09) = 5.103 / 1.98 = 2.577, which rounds to 2.6.

AI explanation

The surface area of the cube gives a side length of 0.9 m, since 6 times the side squared equals 4.86. Melting it gives a cylinder with the same volume of 0.729 m3, calculated as 0.9 cubed. Using the cylinder volume formula of pi times the radius squared times the height, we set (22/7) times 0.3 squared times the height equal to 0.729. Solving for the height gives 2.6 m.

Keep practicing — related questions