The edge of one cube is 4 times the edge of the second. How many times: 1) the surface area of the first cube

| August 19, 2021 | education

The edge of one cube is 4 times the edge of the second. How many times: 1) the surface area of the first cube is greater than the surface area of the second; 2) the volume of the first cube is greater than the volume of the second

1) The area of the cube S = 6 * a ^ 2, where a is the edge of the cube, a1 = 4 * x, a2 = x,
S1 = 6 * (4x) ^ 2 = 6 * 4 ^ 2 * x ^ 2 = 96 * x ^ 2,
S2 = 6 * x ^ 2,
Determine the ratio between the surface areas of the cubes:
(96 * x ^ 2) / (6 * x ^ 2) = 16,
2) The volume of the cube V = a ^ 3,
V1 = (4 * x) ^ 3 = (4 ^ 3) * (x ^ 3) = 64 * x ^ 3,
V2 = x ^ 3,
Determine the ratio between the volumes of the cubes:
(64 * x ^ 3) / (x ^ 3) = 64,
Answer: the surface area of the first cube is 16 times greater than the surface area of the second, the volume of the first cube is 64 times greater than the volume of the second.



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