Question

After taking part in a competition, Eva received a gold medal. She measured the medal and calculated that it has an area of 50.24 square centimeters. What is the medal's circumference?
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Answer 1

Answer:

25.12 cm

Step-by-step explanation:

Based of the assumption that the medal is circular.

From the properties of curves :

• Area of circle = πr^2
• Circumference of circle = 2πr

*r is the radius of that circle.

Here, let the radius of medal be a.

Area of medal = area of a circular object = 50.24 cm^2

= > πa^2 = 50.24 cm^2

= > a^2 = 50.24 / π cm^2

= > a^2 = 50.24 / 3.14 cm^2

= > a^2 = 16 cm^2

= > a = 4 cm

= > 2πa = 2π4 cm

= > Circumference of circle = 8π or (8 x 3.14 = 25.12 cm)

Therefore, circumference of the medal is 25.12 cm.

Answer 2

Answer:

$\large{\underline{\boxed{\mathfrak\blue{Circumference \: of \: medal = 25.12 \: cm }}}}$

Given:-

• Area of circle shaped medal = 50.24 sq.cm

To find:-

• Circumference of medal = ?

Let the radius of medal be r cm.

$\rm We \: know, \\\\\dag \: {\boxed{\rm{Area_{circle} = \pi r^2 }}}$

$\twoheadrightarrow\sf 50.24 = 3.14 \times r^2 \\\\\twoheadrightarrow\sf r^2 = 50.24/3.14 \\\\\twoheadrightarrow\sf r^2 = 16 \\\\\twoheadrightarrow\sf r = \sqrt{16} \\\\\twoheadrightarrow\large{\underline{\boxed{\sf\green{r = 4 \: cm }}}}$

$\therefore\sf {Radius \: of \: medal = 4 \: cm}$

$\rule{100}{2}$

Now,

$\rm We \:know, \\\\\dag \: {\boxed{\rm{Circumference_{circle} = 2\pi r }}}$

$\dashrightarrow\sf Circumference = 2 \times 3.14 \times 4 \\\\\dashrightarrow\large{\underline{\boxed{\sf\blue{Circumference = 25.12 \: cm }}}}$

$\therefore\: {\boxed{\sf\purple{Circumference \: of \: medal = 25.12 \: cm }}}$