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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.
What is the area of the blue glass will be needed to fill each butterfly dot?
Give your answer in terms of pi.

A=◻" inches "^(2)

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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Scale drawings: word problems

Full solution

Q. 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}

Circle Circumference Formula: The circumference $C$ of a circle is given by the formula $C = 2 \pi r$ , where $r$ is the radius. $\newline$ We know $C = 24 \pi$ inches. $\newline$ So, $24 \pi = 2 \pi r$ .
Calculate Radius: Divide both sides by $2 \pi$ to solve for $r$ . $\newline$ $r = \frac{24 \pi}{2 \pi}$ . $\newline$ $r = 12$ inches.
Circle Area Formula: The area $A$ of a circle is given by the formula $A = \pi \cdot r^2$ . Substitute $r = 12$ inches into the formula. $A = \pi \cdot (12)^2$ .
Calculate Area: Calculate the area. $\newline$ $A = \pi \times 144$ . $\newline$ $A = 144\pi$ inches $^2$ .

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\newline

5

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6

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7

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Question

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546.36 = 500(1 + r)

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

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Question

10\text{-kg}

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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

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x

be the height in meters above the ground. Enter

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x_i

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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.)

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