Answer:
141
Step-by-step explanation:
1. The volume of a cylinder is
, where r = radius and h = height. In this case, the height is 5 feet and the radius is 3 feet.
Solving Volume
Step 1: Plug in values
Step 2: Simplify.
Therefore, the volume of the cylinder is 141 ft^3 (but don't put ft^3, as mentioned in the problem).
Have a lovely rest of your day/night, and good luck with your assignments! ♡
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>
Answer number 3
Step-by-step explanation:
The answer is 90. you add them all up and divide it by 4