The problem involves a cube that is cut into 8 equal pieces, and on each piece, a circle of maximum radius is drawn. The sum of the diameters of two circles is given as 8 units.

Step 1: Since the cube is cut into 8 equal pieces, the side of each smaller cube (which is also the diameter of the circle drawn on it) is half of the original cube's side. Given that the sum of the diameters of two circles is 8 units, this means the side of the original cube is 8 units.

Step 2: The maximum volume of a cylinder that can be fit into the cube is given by the formula for the volume of a cylinder, V = πr²h. In this case, the radius r is half the side of the cube, and the height h is the side of the cube. So, r = 8/2 = 4 units and h = 8 units.

Step 3: Substituting these values into the formula gives V = π(4)²(8) = 128π cubic units.

Step 4: The problem asks for one third of this volume, so (1/3)*128π = 42.67π cubic units.

Therefore, none of the given options match the calculated answer.

Question

The problem involves a cube that is cut into 8 equal pieces, and on each piece, a circle of maximum radius is drawn. The sum of the diameters of two circles is given as 8 units.

Step 1: Since the cube is cut into 8 equal pieces, the side of each smaller cube (which is also the diameter of the circle drawn on it) is half of the original cube's side. Given that the sum of the diameters of two circles is 8 units, this means the side of the original cube is 8 units.

Step 2: The maximum volume of a cylinder that can be fit into the cube is given by the formula for the volume of a cylinder, V = πr²h. In this case, the radius r is half the side of the cube, and the height h is the side of the cube. So, r = 8/2 = 4 units and h = 8 units.

Step 3: Substituting these values into the formula gives V = π(4)²(8) = 128π cubic units.

Step 4: The problem asks for one third of this volume, so (1/3)*128π = 42.67π cubic units.

Therefore, none of the given options match the calculated answer.

Knowee AI · Accepted Answer

The problem involves a cube that is cut into 8 equal pieces, and on each piece, a circle of maximum radius is drawn. The sum of the diameters of two circles is given as 8 units.

Step 1: Since the cube is cut into 8 equal pieces, the side of each smaller cube (which is also the diameter of the circle drawn on it) is half of the original cube's side. Given that the sum of the diameters of two circles is 8 units, this means the side of the original cube is 8 units.

Step 2: The maximum volume of a cylinder that can be fit into the cube is given by the formula for the volume of a cylinder, V = πr²h. In this case, the radius r is half the side of the cube, and the height h is the side of the cube. So, r = 8/2 = 4 units and h = 8 units.

Step 3: Substituting these values into the formula gives V = π(4)²(8) = 128π cubic units.

Step 4: The problem asks for one third of this volume, so (1/3)*128π = 42.67π cubic units.

Therefore, none of the given options match the calculated answer.

A cube is cut into 8 pieces equal pieces and nine identical circles of maximum radius drawn on one face of each piece of cube. The sum of diameter of two circles is 8 unit. Find one third of maximum volume of cylinder that can be fit in the initial cube.none of these120 π320 π1152 π1145 π

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