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The horizontal base of a solid prism is an equilateral triangle of side x cm. The sides of the prism are vertical. The height of the prism is h cm and the volume of the prism is 2000 cm³. (i) Express h in terms of x and show that the total surface area of the prism, A cm², is given by √3 24000 √3 (ii) Given that x can vary, find the value of x for which A has a stationary value. (iii) Determine, showing all necessary working, the nature of this stationary value. A

The horizontal base of a solid prism is an equilateral triangle of side x cm. The sides of the prism are vertical. The height of the prism is h cm and the volume of the prism is 2000 cm³. (i) Express h in terms of x and show that the total surface area of the prism, A cm², is given by √3 24000 √3 (ii) Given that x can vary, find the value of x for which A has a stationary value. (iii) Determine, showing all necessary working, the nature of this stationary value. A

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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4. The horizontal base of a solid prism is an equilateral triangle of side x cm. The sides of the prism are vertical. The height of the prism is h cm and the volume of the prism is 2000 cm³. (i) Express h in terms of x and show that the total surface area of the prism, A cm², is given by √3 A = x² + 2 24000 √3 Given that x can vary, find the value of x for which A has a stationary value. (iii) Determine, showing all necessary working, the nature of this stationary value. -x-1
Transcribed Image Text:4. The horizontal base of a solid prism is an equilateral triangle of side x cm. The sides of the prism are vertical. The height of the prism is h cm and the volume of the prism is 2000 cm³. (i) Express h in terms of x and show that the total surface area of the prism, A cm², is given by √3 A = x² + 2 24000 √3 Given that x can vary, find the value of x for which A has a stationary value. (iii) Determine, showing all necessary working, the nature of this stationary value. -x-1
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