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3 years ago

Question 1 (1 point)

Mathematics

2 answers:

svlad2 [7]3 years ago

8 0

Answer:

9π units²

Step-by-step explanation:

To obtain an exact answer, use π, not an approximation such as 3.14.

A = πr² is the appropriate formula.

Here,

A = (3)^2·π units², or 9π units²

BigorU [14]3 years ago

8 0

A=πr2=π·32≈28.27433
If you do pie times 3 squared you get 28.27433

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A closed cylindrical vessel contains a fluid at a 5MPa pressure. The cylinder, which has an outside diameter of 2500mm and a wal

Julli [10]

Answer:

1) Increase in the diameter equals 3.5 mm

2) Increase in the length equals $0.0003724L_{i}$ where $L_{i}$ is the initial length of the vessel.

Step-by-step explanation:

The diametric strain in the vessel is given by

$\epsilon_{D} =\epsilon_{diam}-\nu \epsilon _{axial}$

We have

$\epsilon _{diam}=\frac{\sigma _{hoop}}{E}\\\\\sigma _{hoop}=\frac{\Delta P\times D}{2t}\\\\\therefore \epsilon _{diam}=\frac{\Delta P\times D}{2t\times E}$

Applying values we get

$\therefore \epsilon _{diam}=\frac{5\times 10^{6}\times 2.5}{2\times 20\times 10^{-3}\times 193\times 10^{9}}\\\\\therefore \epsilon _{diam}=\frac{5}{3088}$

Similarly axial strain is given by

$\epsilon _{diam}=\frac{\sigma _{axial}}{E}$

$\sigma _{axial}=\frac{\Delta P\times D}{4t}\\\\\therefore \epsilon _{axial}=\frac{\Delta P\times D}{4t\times E}$

Applying values we get

$\therefore \epsilon _{axial}=\frac{5\times 10^{6}\times 2.5}{4\times 20\times 10^{-3}\times 193\times 10^{9}}\\\\\therefore \epsilon _{diam}=\frac{2.5}{3088}$

Hence The effect of axial strain along the diameter is given by

$-\nu \epsilon _{axial}$

Applying values we get

$-\nu \epsilon _{axial}=-0.27\times \frac{2.5}{3088}=-0.0002185$

hence

$\epsilon _{D} =\frac{5}{3088}-0.0002185\\\\\epsilon =0.00140$

Now by definition of strain we have

$\epsilon _{D} =\frac{D_{f}-D_{i}}{D_{i}}\\\\\therefore D_{f}=D_{i}+\epsilon D_{i}\\\\D_{f}=2.5+0.0014\times 2.5\\\\\therefore D_{f}=2503.5mm$

Increase in the diameter is thus 3.5 mm

Using the same procedure for axial strain we have

$\epsilon_{axial} =\epsilon_{axial}-\nu \epsilon _{diam}$

Applying values we get

$\epsilon_{axial} =\frac{2.5}{3088}-0.27\times \frac{5}{3088}$

$\epsilon_{axial} =0.0003724$

Now by definition of strain we have

$\epsilon _{axial} =\frac{L_{f}-L_{i}}{L_{i}}\\\\\therefore \Delta L=0.0003724L_{i}$

where $L_{i}$ is the initial length of the cylinder.

6 0

4 years ago

1-66.

Andreas93 [3]

The Area of rectangle = 80 unit².

<h3>What is Area of rectangle?</h3>

The area can be defined as the amount of space covered by a flat surface of a particular shape. It is measured in terms of the "number of" square units (square centimeters, square inches, square feet, etc.) The area of a rectangle is the number of unit squares that can fit into a rectangle. Some examples of rectangular shapes are the flat surfaces of laptop monitors, blackboards, painting canvas, etc. You can use the formula of the area of a rectangle to find the space occupied by these objects. For example, let us consider a rectangle of length 4 inches and width 3 inches.

from figure (a)

DE= 40/8 = 5

BC= 100/5 = 20

Now,

AC= AB + BC= 8+ 20 = 28

CE= CD + DE = 10+5= 15

So, area of rectangle

= AC* CE

= 28* 15

= 420

Now, from figure (b)

CD= 24/12= 2

DE= 12/4 = 3

AC= AB+ BC= 14+ 4= 16

CE= CD + DE= 2+3 = 5

So, Area of rectangle= 16*5 = 80 unit²

Learn more about area of rectangle here:

brainly.com/question/237997

#SPJ1

7 0

2 years ago