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Figure 3 shows a solid cuboid which is 5x cm wide, 8x cm long and 7 cm tall. The volume of the cuboid is 67600 cm³. Express h in terms of x and hence show that the surface area, A, of the cuboid is given by A = 43940 x + 80x² (b) Use calculus to find the value of x which gives the minimum surface area and confirm that your value of x gives a minimum.

Figure 3 shows a solid cuboid which is 5x cm wide, 8x cm long and 7 cm tall. The volume of the cuboid is 67600 cm³. Express h in terms of x and hence show that the surface area, A, of the cuboid is given by A = 43940 x + 80x² (b) Use calculus to find the value of x which gives the minimum surface area and confirm that your value of x gives a minimum.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(a) 5x cm A = Figure 3 Figure 3 shows a solid cuboid which is 5x cm wide, 8x cm long and h cm tall. The volume of the cuboid is 67600 cm³. Express h in terms of x and hence show that the surface area, A, of the cuboid is given by 43940 8x cm + 80x² ½ cm (b) Use calculus to find the value of x which gives the minimum surface area and confirm that your value of x gives a minimum.
Transcribed Image Text:(a) 5x cm A = Figure 3 Figure 3 shows a solid cuboid which is 5x cm wide, 8x cm long and h cm tall. The volume of the cuboid is 67600 cm³. Express h in terms of x and hence show that the surface area, A, of the cuboid is given by 43940 8x cm + 80x² ½ cm (b) Use calculus to find the value of x which gives the minimum surface area and confirm that your value of x gives a minimum.
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