Triangle FBT is similar to triangle ADQ with a scale factor of 5/3. AD = 9; BF = 15, DQ = 6; BT = 10, FT = 21; AQ = 12.6
∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°
<h3>What are
similar triangles?</h3>
Similar triangles are triangles that have the same shape and the ratio of their corresponding sides are in the same proportion. Corresponding angles are equal.
triangle FBT is similar to triangle ADQ with a scale factor of 5/3.
AD = 9; BF = 9 * 5/3 = 15
DQ = 6; BT = 6 * 5/3 = 10
FT = 21; AQ = 21 * 3/5 = 12.6
∠F = ∠A = 40°, ∠Q = ∠T = 55°, ∠B = ∠D = 85°
Find out more on similar triangles at: brainly.com/question/2644832
Answer:
SA =64 pi units ^2
Step-by-step explanation:
The surface area of a sphere is given by
SA = 4 pi r^2
SA = 4 * pi * 4^2
SA =64 pi
SA =200.96
The volume as a function of the location of that vertex is
... v(x, y, z) = x·y·z = x·y·(100-x²-y²)
This function is symmetrical in x and y, so will be a maximum when x=y. That is, you wish to maximize the function
... v(x) = x²(100 -2x²) = 2x²(50-x²)
This is a quadratic in x² that has zeros at x²=0 and x²=50. It will have a maximum halfway between those zeros, at x²=25. That maximum volume is
... v(5) = 2·25·(50-25) = 1250
The maximum volume of the box is 1250 cubic units.
