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nikklg [1K]
3 years ago
8

A square with an area of 49 in2 is rotated to form a cylinder. What is the volume of the cylinder

Mathematics
1 answer:
svlad2 [7]3 years ago
8 0
<span>343 pi in^3 ; exact volume 1078 in^3 ; Approximate volume Since it's not specified, I will assume the axis of rotation will be one edge of the square. With that in mind, here's the solution. Since the shape specified is a square with an area of 49 in^2, the length of any edge will be sqrt(49) = 7 inches. Since we're rotating along one edge, we will create a cylinder with a radius of 7 inches and a height of 7 inches. The volume will be the area of a circle with a 7 inch radius multiplied by the height of the cylinder. So V = pi*h*r^2 V = pi*7*7^2 V = pi*7*49 V = pi*343 V = 343pi V = 1077.56628; approximately. So the exact volume is 343pi in^3 and an approximate volume is 1078 in^3</span>
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Show that x + y : x - y= 3 : 2
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x + y : x - y = (5/2+1/2) : (5/2-1/2)

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Step-by-step explanation:

Given

x + y : x - y = 3 : 2

As

x + y = 3

x - y = 2

Solving to find x and y

\begin{bmatrix}x+y=3\\ x-y=2\end{bmatrix}

x-y=2

-

\underline{x+y=3}

-2y=-1

\begin{bmatrix}x+y=3\\ -2y=-1\end{bmatrix}

solve for y

-2y=-1

Divide both sides by 2

\frac{-2y}{-2}=\frac{-1}{-2}

y=\frac{1}{2}

\mathrm{For\:}x+y=3\mathrm{\:plug\:in\:}y=\frac{1}{2}

x+\frac{1}{2}=3

x+\frac{1}{2}-\frac{1}{2}=3-\frac{1}{2}

x=\frac{5}{2}

so

x=\frac{5}{2},\:y=\frac{1}{2}

Thus,

x + y : x - y = (5/2+1/2) : (5/2-1/2)

x + y : x - y = 3 : 2

Therefore,  x + y : x - y= 3 : 2 is proved.

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3 years ago
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