Question

The figure shows the the cross section of the interior part of a thermos flask, the top part is a trapezium, the middle part is rectangle, and the bottom part is a semi circle, if ce=20cm , bc=25cm , ab=gf=13cm, ag=10cm and an=12cm , find the perimeter of the cross section and area of the cross section

Answer 1

Perimeter of the cross section = 120.4 cm

Area of the cross section = 837 cm²  

Solution:

The image of the question is attached below.

CE = 20 cm, BC = 25 cm, AB = GF = 13 cm

AG = 10 cm, AN = 12 cm

Diameter of the semi-circle = 20 cm

Radius of the semi-circle = 20 ÷ 2 = 10 cm

Perimeter of CE = πr

                           = 3.14 × 10

                           = 31.4 cm

Perimeter of the cross section = AB + BC + CE + EF + FG + GA

                                                   = 13 cm + 25 cm + 31.4 + 25 + 13 + 13

                                                   = 120.4 cm

Perimeter of the cross section = 120.4 cm

Area of the trapezium = $\frac{1}{2} \times\text{sum of the parallel side}\times\text{height}$

                                     $=\frac{1}{2} \times(10+20)\times12$

                                     = 180 cm²

Area of the rectangle = length × width

                                    = 25 × 20

                                    = 500 cm²

Area of the semi-circle = $\frac{1}{2}\times \pi r^2$

                                      $=\frac{1}{2}\times 3.14\times 10^2$

                                      = 157 cm²

Area of the cross section = Area of the trapezium + Area of the rectangle

                                              + Area of the semi-circle

                                          = 180 cm² + 500 cm² + 157 cm²

                                          = 837 cm²

Area of the cross section = 837 cm²  

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