Express the edge length of a cube as a function of the cube's diagonal length d. Then express the surface area & volume of t he cube as a function of the diagonal length.
2 answers:
D = sqrt(3s^2) where s is the length of the side. Solving for s, <span>3s^2 = d^2 iff </span> <span>s^2 = d^2 / 3 iff </span> <span>s = sqrt(d^2 / 3) </span> <span>= d / sqrt(3) or d sqrt(3) / 3 </span> <span>Surface area of the cube = 6 s^2. Thus, </span> <span>A = 6 (d / sqrt(3))^2 </span> <span>= 6d^2 / 3 </span> <span>= 2d^2 </span> <span>Volume = s^3. Thus, </span> <span>V = (d / sqrt(3))^3 </span> <span>= d^3 / 3sqrt(3) </span> <span>= d^3 sqrt(3) / 9</span>
D = sqrt(3s^2) , <span>3s^2 = d^2 </span> <span>s^2 = d^2 / 3 </span> <span>s = sqrt(d^2 / 3) </span> <span>= d / sqrt(3) </span> now we will find surface area therefore <span>Surface area of the cube = 6 s^2.</span> <span>Area = 6 (d / sqrt(3))^2 </span> <span>= 6d^2 / 3 </span> <span>= 2d^2 </span> now we shall find volume <span>V = s^3.</span> <span>V = (d / sqrt(3))^3 </span> <span>= d^3 / 3sqrt(3) </span> <span>= d^3 sqrt(3) /9 hope this helps</span>
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