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Circle $K$ with a radius of $3$ units is shown on a coordinate grid. Circle $K$ is dillated by a scale factor of $\frac{5}{3}$ , centered at the origin, to map to Circle $M$ . $\newline$ Complete the statement. $\newline$ The area of the Circle $M$ is $\pi$ units $^2$ .

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Scale drawings: word problems

Full solution

Q. Circle

K

with a radius of

3

units is shown on a coordinate grid. Circle

K

is dillated by a scale factor of

\frac{5}{3}

, centered at the origin, to map to Circle

M

.

\newline

Complete the statement.

\newline

The area of the Circle

M

is

\pi

units

^2

.

Identify Radius and Scale Factor: Identify the original radius of Circle $K$ and the scale factor for the dilation. $\newline$ Circle $K$ has a radius of $3$ units. The scale factor for the dilation is $\frac{5}{3}$ .
Calculate New Radius: Calculate the new radius of Circle $M$ after the dilation. $\newline$ The new radius of Circle $M$ is the original radius of Circle $K$ multiplied by the scale factor. So, the new radius is $3$ units $\times \left(\frac{5}{3}\right) = 5$ units.
Calculate Area of Circle M: Calculate the area of Circle M using the new radius. $\newline$ The area of a circle is given by the formula $A = \pi r^2$ , where $r$ is the radius of the circle. Substituting the new radius of Circle M into the formula gives us $A = \pi \times (5 \text{ units})^2 = \pi \times 25 \text{ units}^2$ .
Write Complete Statement: Write the complete statement for the area of Circle M. $\newline$ The area of Circle M is $25\pi$ square units.

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