For the derivative tests method, assume that the sphere is centered at the origin, and consider the
circular projection of the sphere onto the xy-plane. An inscribed rectangular box is uniquely determined
1
by the xy-coordinate of its corner in the first octant, so we can compute the z coordinate of this corner
by
x2+y2+z2=r2 =⇒z= r2−(x2+y2).
Then the volume of a box with this coordinate for the corner is given by
V = (2x)(2y)(2z) = 8xy r2 − (x2 + y2),
and we need only maximize this on the domain x2 + y2 ≤ r2. Notice that the volume is zero on the
boundary of this domain, so we need only consider critical points contained inside the domain in order
to carry this optimization out.
For the method of Lagrange multipliers, we optimize V(x,y,z) = 8xyz subject to the constraint
x2 + y2 + z2 = r2<span>. </span>
Opposite angles of parallelogram are equal.
sum of interior angles of parallelogram is 360 degrees.
Therefore,
A + B + C + D = 360
x + 145 + x + 145 = 360
x = 35
Therefore angle C is 35 degrees
Answer:
81 units³
Step-by-step explanation:
V = Length x Widht x Height
= 9 x 3 x 3
= 81 units³
Answer:
B is the answer
Step-by-step explanation:
