Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 121 square meters.
A)Dimensions:
B)Dimensions:
C)Dimensions:
D)Dimensions:
E)Dimensions:

Question

Determine the dimensions of a rectangular solid (with a square base)with maximum volume if its surface area is 121 square meters. ​
A)Dimensions: 
B)Dimensions: 
C)Dimensions: 
D)Dimensions: 
E)Dimensions:

Quizplus · Accepted Answer

Let the side length of the square base be x and the height be h. 
The surface area is given by 2x^2 + 4xh = 121, which simplifies to x^2 + 2xh = 60. 
We want to maximize the volume, which is given by V = x^2h. 
Using the equation x^2 + 2xh = 60, solve for h in terms of x: h = (60 - x^2)/(2x). 
Substitute this into the equation for volume to get V = x^2(60 - x^2)/(2x). 
Simplify to V = (1/2)x(60x - x^3). 
To find the maximum volume, take the derivative of V with respect to x and set it equal to 0: 
dV/dx = 30x - 1.5x^2 = 0. 
Solving for x, we get x = 20. 
Substitute this value back into the equation for h to get h = 10. 
Therefore, the dimensions are 20 x 20 x 10.

Determine the Dimensions of a Rectangular Solid (With a Square