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4 years ago

The radius of the base of a cylinder is 28 cm and its height is 48 cm. Find the surface area of the cylinder in terms of π. 4,23

2π cm2 4,256π cm2 4,208π cm2 4,228π cm2

Mathematics

1 answer:

spin [16.1K]4 years ago

4 0

$\bf \textit{total surface area of a cylinder}\\\\
SA=2\pi r(h+r)~~
\begin{cases}
r=radius\\
h=height\\
-----\\
r=28\\
h=48
\end{cases}\implies SA=2\pi (28)(48+28)
\\\\\\
SA=56\pi (76)\implies SA=4256\pi$

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The vertices of a backyard are W(10,30),X(10,100),Y(110,100),Z(50,30). The coordinates are measured in feet. The line segment XZ

MariettaO [177]

Given vertices W(10,30), X(10,100), Y(110,100), Z(50,30) of a backyard, find distances WX, XY, YZ, ZW and XZ:

1. $WX=\sqrt{(10-10)^2+(30-100)^2}=\sqrt{70^2}=70\ ft;$

2. $XY=\sqrt{(110-10)^2+(100-100)^2}=\sqrt{100^2}=100\ ft;$

3. $YZ=\sqrt{(110-50)^2+(100-30)^2}=\sqrt{60^2+70^2}=10\sqrt{85}\ ft;$

4. $ZW=\sqrt{(50-10)^2+(30-30)^2}=\sqrt{40^2}=40\ ft;$

5. $XZ=\sqrt{(10-50)^2+(100-30)^2}=\sqrt{40^2+70^2}=10\sqrt{65}\ ft.$

Then:

1. the area

$A_{WXZ}=\sqrt{\frac{70+40+10\sqrt{65}}{2}\\\cdot (\frac{70+40+10\sqrt{65}}{2}-70)\cdot (\frac{70+40+10\sqrt{65}}{2}-40)\cdot (\frac{70+40+10\sqrt{65}}{2}-10\sqrt{65})}=\\ \\=1400\ ft^2.$

2. the area

$A_{XYZ}=\sqrt{\frac{100+10\sqrt{85}+10\sqrt{65}}{2}\cdot (\frac{100+10\sqrt{85}+10\sqrt{65}}{2}-100)}\cdot\\ \\\cdot\sqrt{(\frac{100+10\sqrt{85}+10\sqrt{65}}{2}-10\sqrt{85})\cdot (\frac{100+10\sqrt{85}+10\sqrt{65}}{2}-10\sqrt{65})}=3500\ ft^2.$

Then

$\dfrac{A_{XYZ}}{A_{WXZ}}=\dfrac{3500}{1400}=2.5$ times greater.

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4 years ago

Math help............

Romashka-Z-Leto [24]

<h3>Answers:</h3>

The value x is x = 15

The three sides of the triangle are

x+10 = 25

2x-5 = 25

3x-15 = 30

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Work Shown:

The curved angle markers indicate those two angles are the same measure. The sides opposite those angles are the same length. So 2x-5 and x+10 are the same value

2x-5 = x+10

2x-x = 10+5

x = 15

Once we know x, we can find the length of each side

x+10 = 15+10 = 25

2x-5 = 2*15-5 = 30-5 = 25

This also helps confirm we have the right x value (since we got the same value for each expression)

3x-15 = 3*15-15 = 45-15 = 30

This is an isosceles triangle because exactly two sides are the same length.

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