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Anestetic [448]
1 year ago
6

A rectangle has dimensions of 9 in. by 8 in. Find the exact volume (in cubic inches) of the solid of revolution formed when the

rectangle is rotated about its 8 in. side.Incorrect: Your answer is incorrect.in3

Mathematics
1 answer:
Sauron [17]1 year ago
4 0

V = 162π in^3

Explanation:

Since rotation a rectangle on its side result to a cylinder.

We'll use the formula for the volume of a cylinder with 8in being the height (since the rectangle is rotated around that side) and 9 in as the diameter.

Data:

Radius : r = diameter / 2 = 9/2 = 4.5 in

Height : h = 8 in

Formula:

V=\pi *r^2*h

Solution:

\begin{gathered} V=\pi *4.5^2*8 \\ V=162\pi\text{ }in^3 \end{gathered}

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Answer:

30

Step-by-step explanation:

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using pythagoras theorem

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2 years ago
The rectangle shown has a perimeter of 146 cm and the given area. Its length is 7 more than five times its width. Write and solv
dangina [55]

Answer:

System of equations:

L = 5W + 7

2W + 2L = P

L = 62 cm

W = 11 cm

Step-by-step explanation:

Given the measurements and key words/phrases in the problem, we can set up two different equations that can be used to find both variables, length and width, of the rectangle.  

The formula for perimeter of a rectangle is:  2W + 2L = P, where W = width and L = length.  We also know that the L is '7 more than five times its width'.  This can be written as:  L = 5W + 7.  Using this expression for the value of 'L', we can use the formula for perimeter and solve for width:

2W + 2(5W + 7) = 146

Distribute:  2W + 10W + 14 = 146

Combine like terms:  12W + 14 = 146

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Divide 12 by both sides:  12W/12 = 132/12 or W = 11

Put '11' in for W in the equation for 'L':  L = 5(11) + 7 or L = 55 + 7 = 62.

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3 years ago
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