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3 years ago

The ratio of the volume of two cubes is 216 to 64. What is the ratio of their surface/

1 answer:

5 0

The volume of a cube is V=s^3, so s=V^(1/3).

The area of a cube is A=6s^2, using s found above we have:

A=6(V^(2/3))

Let V and S be the volume and area of the larger and v and s be the volume and area of the smaller cube.

A:a

6(V^(2/3)):6(v^(2/3))

V^(2/3):v^(2/3), we are given that V=216 and v=64 so

216^(2/3):64^(2/3)

36:16

9:4

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B. False, because

$(a^2-b^2)(c^2+d^2)=a^2c^2+a^2d^2-b^2c^2-b^2d^2\\ \\(ac-bd)^2-(ad+bc)^2=a^2c^2-2abcd+b^2d^2+a^2d^2+2abcd+b^2c^2=\\=a^2c^2+b^2d^2+a^2d^2+b^2c^2\\ \\a^2c^2+a^2d^2-b^2c^2-b^2d^2\neq a^2c^2+b^2d^2+a^2d^2+b^2c^2$

C. False, because

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D. True, because

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