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Montano1993 [528]
3 years ago
10

A cylinder has a height of 1.2 cm and the following base.

Mathematics
2 answers:
netineya [11]3 years ago
7 0

Answer:

94.2 cubic mm

Step-by-step explanation:

The volume for a cylinder is

V=\pi r^2h

We can use 3.1415 for pi,

r = 5

h = 1.2

Filling in then:

V=3.1415(5^2)(1.2)

and

V=3.1415(25)(1.2) so

V=94.2mm^3

Just multiply all those numbers together.

Alex Ar [27]3 years ago
5 0

Answer:

V=942\ mm^{3}

Step-by-step explanation:

Hello

I think I can help you with this

the Volume of a cylinder is given by:

V=\pi *radius^{2} *h

in these exercises be careful with the units of measure, they must be the same units of length in this case mm

Step 1

convert 1.2 cm into mm

using a rule of three

1 cm ⇔ 10 mm

1.2 cm ⇔x mm?

\frac{1\ cm}{10\ mm}=\frac{1.2 cm}{x}\\solve\ for\ x\\\\\frac{x*1\ cm}{10\ mm}=1.2 cm\\x=\frac{1.2\ cm*10\ mm}{1\ cm} \\x=12\ mm\\

so, height is 12 mm

Step 2

put the values into the equation

Let

radius= 5 mm

height= 12 mm

V=\pi *radius^{2} *h\\V=\pi *(5\ mm)^{2} *12\ mm\\V=\pi*300\ mm^{3}\\V=942.47\ mm^{3}

Have a nice day

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3 years ago
A plane is flying east at 115 m/s. The wind accelerates it at 2.88 m/s^2 directly northwest. After 25.0 s, what is the direction
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<h3>Answer: 38.5 degrees</h3>

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

Explanation:

The east direction is the vector < 1, 0 >

If the plane is flying in this direction, we want a vector to point in the direction of < 1, 0 > and we want it to have a magnitude of r = 115. So we simply scale this vector with scale factor 115

< 1, 0 > turns into < 115, 0 >

I multiplied both coordinates by 115.

If we do not account for the wind, the plane's velocity vector is < 115, 0 >

--------------------------------------------

The wind's velocity vector is a bit trickier. We're told that the magnitude of the wind's acceleration vector is 2.88 m/s^2. This means every second, the wind's speed is increasing by 2.88 m/s. After 25 seconds, the speed of the wind is 25*2.88 = 72 m/s, which is the magnitude of the wind vector.

So r = 72

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The x and y components of the wind's velocity vector is

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-----------------------------------------------------

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Vector addition will yield the resultant vector. This vector is the true direction of where the plane is going after we account for the wind speed. Without the wind speed, the plane will go directly east. However, with the wind speed, the plane will go in the direction of the red vector arrow (see diagram below).

So we have,

< 115, 0 > +  =

+ = < 64.1, 50.9>

The plane's resultant vector is approximately which is the velocity vector of the plane after we account for wind.

-----------------------------------------------------

The last step is to compute the theta of this resultant vector

theta = arctan(b/a)

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theta = 38.452096

theta = 38.5

This theta value is represented of the red vector in the diagram below.

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The significance level is, <em>α</em> = 0.05.

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