A cube has a side length of 5 cm. Determine the surface area of the largest pyramid that will fit inside the cube. Round if necessary.

The surface area of the pyramid is 80.9 cm²

Step-by-step explanation:

The side length, s of the cube is given as 5 cm

Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm

The height, h of the largest pyramid = The height of the cube = 5 cm.

The surface area of a pyramid =  Area of base, A + 1/2 × Perimeter of base, P × Slant height, S

The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5

The perimeter of the base = 4×5 = 20 cm

The area of the base = 5×5 = 25 cm²

The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².

The surface area of a pyramid =  80.9 cm².

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step-by-step explanation: