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>
You might be interested in
Answer:
That would be 20.
Step-by-step explanation:
Hope this helps
4(3w+5)-2w=70
10w+20=70
10w+20-20=70-20
10w=50
10w/10=50/10
w=5
Hmm I’ve done this before but I can’t remember sorry but I will try and think
The x intercept of the line is at x = 10.
The x intercept is always the value of x when all other values are equal to 0. So in this case, we put 0 in for t and then solve.
-2x + 5t = -20
-2x + 5(0) = -20
-2x = -20
x = 10
The correct answer is c. 16.6
Explain
The triangle left side
Opposite side= hypotheses x sin 0
Plugin
Opposite side = 39 x sin 43
39 x 0.68
26.60
The right side
Opposite side = adjective side x tan0
Opposite side = 26.60 x tan 32
26.60 x 0.62
X= 16.6
Hope this help you :D
