A sphere with diameter 1 unit is enclosed in a cube of side 1 unit each. Find the unoccupied volume remaining inside the cube. a. ¼ b. 2π c. π/6-1 d. 1-π/4 e. 1-π/6
Question
A sphere with diameter 1 unit is enclosed in a cube of side 1 unit each. Find the unoccupied volume remaining inside the cube. a. ¼ b. 2π c. π/6-1 d. 1-π/4 e. 1-π/6
Solution
Step 1: First, we need to find the volume of the cube. The formula for the volume of a cube is side^3. Since the side of the cube is 1 unit, the volume of the cube is 1^3 = 1 cubic unit.
Step 2: Next, we need to find the volume of the sphere. The formula for the volume of a sphere is 4/3 * π * (diameter/2)^3. Since the diameter of the sphere is 1 unit, the radius is 1/2 unit. So, the volume of the sphere is 4/3 * π * (1/2)^3 = π/6 cubic units.
Step 3: Finally, we subtract the volume of the sphere from the volume of the cube to find the unoccupied volume inside the cube. So, the unoccupied volume is 1 - π/6 cubic units.
So, the answer is e. 1-π/6.
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