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2 years ago

The figure is made up of two shapes, a semicircle and a rectangle.What is the exact perimeter of the figure?

Mathematics

2 answers:

grandymaker [24]2 years ago

7 0

Perimeter of circular area = πr = 3.14 * 10 = 31.4 mm

Perimeter of rectangular area = 30 + 20 + 30 = 80 mm

Total Perimeter = 80 + 31.4 = 111.4

In short, Your Answer would be 111.4 mm

Hope this helps!

Svetllana [295]2 years ago

7 0

Perimeter of a rectangle =2(w+l)=2(50)=100mm

perimeter of a semicircle =circumference of a semicircle=2π2/2=2π*10/2

here d=20 so r=d/2=10mm

perimeter of a semicircle=10πmm=31.4 mm

perimeter of a whole fig is 31.4+100=131.4mm

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============================================

Work Shown:

$P_1*V_1 = P_2*V_2 \ \text{ ... Boyle's Law}\\\\4.5*1.5 = P_2*3.5\\\\6.75 = P_2*3.5\\\\P_2*3.5 = 6.75\\\\P_2 = \frac{6.75}{3.5}\\\\P_2 \approx 1.92857142857142\\\\P_2 \approx 1.9\\\\$

If the volume is 3.5 liters, then the pressure is approximately 1.9 atm.

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-----------

As a check,

$P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.9*3.5\\\\6.75 \approx 6.65\\\\$

We don't get the exact thing on both sides, but the two sides are close enough. We have rounding error due to P2 being not exact.

A more accurate check could be

$P_1*V_1 = P_2*V_2\\\\4.5*1.5 \approx 1.92857*3.5\\\\6.75 \approx 6.749995\\\\$

which has the two sides much closer to one another. This helps us verify the answer.

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