Side of cube=6cm Sphere is placed in cube.Calculate volume of cube.Calculate volume of sphere.What percentage of the space in the cube does the sphere occupy?
V cube = 6 * 6 * 6 = ?
Have no idea of dimensions of sphere. Does it touch the sides of the cube? If so, r = 3.
V sphere = 4/3 π r^3 = ?
V sphere/V cube = ?
To calculate the volume of a cube, we need to know the length of one side.
In this case, the side of the cube is given as 6 cm. To find the volume of the cube, we use the formula:
Volume = side^3
Substituting the value, we get:
Volume = 6 cm * 6 cm * 6 cm = 216 cubic cm
So, the volume of the cube is 216 cubic cm.
To calculate the volume of a sphere, we need to know the radius.
In this case, we can calculate the radius using the formula:
Radius = side / 2
Substituting the value, we get:
Radius = 6 cm / 2 = 3 cm
To find the volume of the sphere, we use the formula:
Volume = (4/3) * π * radius^3
Substituting the value, we get:
Volume = (4/3) * π * 3 cm^3 = 36π cubic cm (approx.)
So, the volume of the sphere is approximately 36π cubic cm.
To calculate what percentage of the space in the cube the sphere occupies, we can compare the volumes.
Percentage = (Volume of sphere / Volume of cube) * 100
Substituting the values, we get:
Percentage = (36π / 216) * 100 ≈ 52.36%
Therefore, the sphere occupies approximately 52.36% of the space in the cube.