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notka56 [123]
3 years ago
11

A cylinder has radius r and height h. A. How many times greater is the surface area of a cylinder when both dimensions are multi

plied by a factor of 2? 3? 5? 10? B. Describe the pattern in part (a).
Mathematics
1 answer:
Ierofanga [76]3 years ago
3 0

Answer: A. Factor 2 => 4x greater

                   Factor 3 => 9x greater

                   Factor 5 => 25x greater

Step-by-step explanation: A. A cylinder is formed by 2 circles and a rectangle in the middle. That's why surface area is given by circumference of a circle, which is the length of the rectangle times height of the rectangle, i.e.:

A = 2.π.r.h

A cylinder of radius r and height h has area:

A_{1} = 2πrh

If multiply both dimensions <u>by a factor of 2</u>:

A_{2} = 2.π.2r.2h

A_{2} = 8πrh

Comparing A_{1} to A_{2} :

\frac{A_{2}}{A_{1}} = \frac{8.\pi.rh}{2.\pi.rh} = 4

Doubling radius and height creates a surface area of a cylinder 4 times greater.

<u>By factor 3:</u>

A_{3} = 2.\pi.3r.3h

A_{3} = 18.\pi.r.h

Comparing areas:

\frac{A_{3}}{A_{1}} = \frac{18.\pi.r.h}{2.\pi.r.h} = 9

Multiplying by 3, gives an area 9 times bigger.

<u>By factor 5</u>:

A_{5} = 2.\pi.5r.5h

A_{5} = 50.\pi.r.h

Comparing:

\frac{A_{5}}{A_{1}} = \frac{50.\pi.r.h}{2.\pi.r.h} = 25

The new area is 25 times greater.

B. By analysing how many times greater and the factor that the dimensions are multiplied, you can notice the increase in area is factor². For example, when multiplied by a factor of 2, the new area is 4 times greater.

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alexdok [17]

Answer:

x = -3 cos (\frac{\pi}{2})= 0

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And then the rectangular coordinates for this case are :

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Step-by-step explanation:

We have the following point given P = (-3, \frac{\pi}{2}) and we want to conver from polar to rectangular coordinates and we need to use the following formulas:

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Replacing we got:

x = -3 cos (\frac{\pi}{2})= 0

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And then the rectangular coordinates for this case are :

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4 0
3 years ago
Mrs. Dimitri purchased a case of yogurt cups. Out of every 10 yogurt cups, 6 are strawberry.
emmasim [6.3K]

Answer:

1) The fraction of yogurt cups that are strawberry is 18/30. (True)

2) There are a total of 60 strawberry yogurt cups. (False)

3) 60% of the yogurt cups are strawberry. (True)

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Step-by-step explanation

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1) The fraction of yogurt cups that are strawberry,

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2) There are a total of 60 strawberry yogurt cups,

the total number of yogurt cups is 30 while that of strawberry is 18

3) 60% of the yogurt cups are strawberry,

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4) 30% of the yogurt cups are NOT strawberry,

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Answer:

mi español no es tan bueno si hay algún error en esto entonces lo siento

cursos en diferencial = a, b, c

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Step-by-step explanation:

márcame como el más inteligente

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