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Gelneren [198K]
3 years ago
7

Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area and volume of the

cube as a function of the diagonal length.
a. A function for the edge length of a cube is L(d) = _________________
b. A function for the surface area of a cube is Ald) = _____________
c. A function for the volume of a cube is V(d) = ________________
Mathematics
1 answer:
Damm [24]3 years ago
8 0

Answer:

Step-by-step explanation:

If L is the length of a side, the longest diagonal in the cube is

d = √(L² + L² + L²) = √(3L²) = L√3

meaning

a) L(d) = d/√3 = ⅓d√3

b) A(d) = 6(L(d))² = 6(⅓d√3)² = 6(⅟₉d²(3)) = 2d²

c) V(d) = (L(d))³ = (⅓d√3)³ = ⅟₂₇d³3√3 = ⅟₉d³√3

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