Dr. J's Maths.com
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Calculus - Differentiation - Applied max/min questions.
Type 3: Basic 3D shapes - Test Yourself 1 - Solutions.


 

Boxes 1. (i)

(ii)

  2. (i) The three horizontal pieces are each 2x × y cm2 in area.

The two ends are each xy cm2 in area and the back panel is 2x×x cm2.

Hence the use of the pineboard is

24 = 3(2xy) + 2(xy) + 2x2 = 8xy + 2x2.

(ii) Volume = x × 2x × y = 2x2y.

But from part (i)

(iii)

  3. (i) (ii)
  4. (i) To find the area of the trapezium cross section, we need the width at the top. This width has a central length equal to the base "a" plus two lengths from isosceles triangles note the angle given is 45°). So those lengths are both h.

Top = a + h + h = a + 2h = 60.

(ii)

(iii)

  5. (i)

Take the lower left corner of the shape and note the mark-up in the diagram above.

(ii)

(iii)

Cones. 6.

  7.
  8. (i)

(ii)

(iii)

  9.
Cylinders.

10.

  11.
  12. (i)

(ii)

(iii)

(iv)

 

13.

 

14. (i)

(ii)