Question

The King and the Queen want to decorate the castle for Rapunzel´s birthday. They should balance 3 aluminum spheres for every iron cube. The cubes have sides with area 36 cm^2. Which should be the radio of each sphere?

a) 1:3
b) 2:3
c) 3:2
d) 1:2

Answer 1

To balance the aluminum spheres and iron cubes, the radius of each sphere should be approximately 1.15 cm.

Step-by-step explanation:

To balance the aluminum spheres and iron cubes, there should be 3 aluminum spheres for every iron cube. The area of each side of the iron cube is 36 cm^2. To determine the radius of each sphere, we need to find the volume of the sphere and the volume of the cube. The volume of the cube is (side length)^3, which is 36 cm^3. Since the spheres and cubes are balanced in a 3:1 ratio, the volume of each sphere should be 1/3 of the cube's volume, which is 12 cm^3. The formula for the volume of a sphere is (4/3)π(radius)^3, so we can solve for the radius by equating the formula to 12 cm^3. By simplifying the equation, we find that the radius of each sphere is approximately 1.15 cm.