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A park has a large circle painted in the middle of the playground area. The circle is divided into 4 equal sections, and each section is painted a different color. The radius of the circle is 10 meters.
What is the area
A of each section of the circle?
Give your answer in terms of pi.

A=◻quad bar(" +x. ")m^(2)

A park has a large circle painted in the middle of the playground area. The circle is divided into $4$ equal sections, and each section is painted a different color. The radius of the circle is $10$ meters. $\newline$ What is the area $A$ of each section of the circle? $\newline$ Give your answer in terms of pi. $\newline$ $A=\square$ $\mathrm{m}^{2}$

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Scale drawings: word problems

Full solution

Q. A park has a large circle painted in the middle of the playground area. The circle is divided into

4

equal sections, and each section is painted a different color. The radius of the circle is

10

meters.

\newline

What is the area

A

of each section of the circle?

\newline

Give your answer in terms of pi.

\newline

A=\square

\mathrm{m}^{2}

Calculate total circle area: First, calculate the area of the whole circle using the formula $A = \pi r^2$ , where $r$ is the radius. $A = \pi \times (10 \text{ meters})^2$ $A = \pi \times 100 \text{ meters}^2$
Divide total area by $4$ : Since the circle is divided into $4$ equal sections, divide the total area by $4$ to find the area of one section. $\newline$ Area of one section = $(\pi \times 100 \text{ meters}^2) / 4$ $\newline$ Area of one section = $25\pi \text{ meters}^2$

More problems from Scale drawings: word problems

Question

A scale on a blue print drawing of a house shows that

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centimeters represents

2

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What number of actual meters are represented by

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centimeters on the blue print?

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The figure below shows a rope that circles the Earth. The radius of the Earth is

6371

\newline

Assuming the rope makes a perfect circle, what is the length of this rope?

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Give your answer in terms of pi.

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Question

An artist is creating a large butterfly sculpture outside a museum. There is a circular dot on each wing made out of a metal ring. The distance around each dot is

24 \pi

inches. The artist plans to fill the inside of each dot with blue colored glass.

\newline

What is the area of the blue glass will be needed to fill each butterfly dot?

\newline

Give your answer in terms of pi.

\newline

A=\square

\text {inches }^{2}

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Question

A baker uses a coffee mug with a diameter of

8 \mathrm{~cm}

to cut out circular cookies from a big sheet of cookie dough.

\newline

What is the area

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of each cookie? Give your answer in terms of pi.

\newline

A=\square

\mathrm{~cm}^{2}

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Question

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\text{ }

square units. Thea drew a scaled version of Rectangle

\text{ }

and labeled it Rectangle

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. What scale factor did Thea use to go from Rectangle

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Question

You pick a card at random, put it back, and then pick another card at random.

\newline

4

\newline

5

\newline

6

\newline

7

\newline

What is the probability of picking a number greater than

5

and then picking a

4

\newline

Write your answer as a percentage.

Posted 1 month ago

Question

Jeanne's bank account earns interest annually. The equation shows her starting balance of

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and her balance at the end of three years,

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r

did Jeanne earn interest?

\newline

546.36 = 500(1 + r)

Posted 1 month ago

Question

Jeanne's bank account earns interest annually. The equation shows her starting balance of

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and her balance at the end of three years,

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. At what rate r did Jeanne earn interest?

\newline

422.78=350(1+r)^{3}

Posted 1 month ago

Question

10\text{-kg}

bucket is lifted from the ground to a height of

14\, \text{m}

at a constant speed with a rope that weighs

0.6\, \text{kg/m}

. Initially the bucket contains

42\, \text{kg}

of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the

14\, \text{m}

level. How much work is done? (Use

9.8\, \text{m/s}^2

g

.) Show how to approximate the required work (in

\text{J}

) by a Riemann sum. (Let

x

be the height in meters above the ground. Enter

x_i^*

x_i

Posted 1 month ago

Question

10-\mathrm{kg}

bucket is lifted from the ground to a height of

14

m at a constant speed with a rope that weighs

0.6 \mathrm{~kg} / \mathrm{m}

. Initially the bucket contains

42

kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the

14-\mathrm{m}

level. How much work is done? (Use

9.8 \mathrm{~m} / \mathrm{s}^{2}

\newline

Show how to approximate the required work (in J) by a Riemann sum. (Let

x

be the height in meters above the ground. Enter

x_{i}^{* *}

x_{i}

\newline

\lim _{n \rightarrow \infty} \sum_{i=1}^{n}\left(\boxed{98+35.28 x_{i}}\right) \Delta x

\newline

Express the work (in J) as an integral in terms of

x

\newline

\int_{0}^{14}(98+35.28 x

\newline

Evaluate the integral (in J). (Round your answer to the nearest integer.)

Posted 1 month ago

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