Dr. J's Maths.com
Where the techniques of Maths
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Calculus - Differentiation - Applied max/min questions.
Type 3: Basic 3D shapes - Test Yourself 2.


 

Boxes 1. A triangular prism has a base in the shape of an equilateral triangle with sides x cm. The length of the prism is y cm. The volume of the prism is 1000 cm3.

(i) Show that .

(ii) Show that the total surface area of the triangular prism can be expressed as .

(iii) Find the value of the x (to the nearest mm) such that the surface area of the prism is mimimised.

Answer.x = 15.9 cm.
  2.
  3. The diagram below shows a rectangular box with a square base having a volume of 500 cm3. The box has no lid.

(i) Show that the surface area of the box can be expressed as

(ii) Find the least area of sheet metal needed to construct this box.

Answer.Min area = 300 cm2 when x = 10.
Cones.  
   
   
Cylinders.