Question

The curves in the below image are perfect semicircles. If the straight line AB measures 18 cm, what is the length (in m) of the curved line of the figure​

Answer 1

The length of the curved line of the figure​ is 0.5652 m.

What is the length of a curved line?

• You'll need a tool called a protractor and some basic information.
• You must also know the diameter of the circle.
• Then, you can apply the following formula: length of an arc = diameter x 3.14 x the angle divided by 360.

What is length of curved surface measured in?

• The length of a curved surface is measured by using metre scale and thread.

What is used to measure a curved line?

• The length of curved line can be measured using a string.

According to the question:

The measure of the curved line can be found out by using the formula of circumference.

They are two perfect semicircles , therefore we can consider it to be one semicircle with radius 18cm as the length of AB is 18cm.

We know that the circumference of a circle is given by :

                                     ⇒ 2πR.          

where, R is the radius.

As given is a semicircle we will divide the formula by 2.

Therefore we get , the circumference of the semicircle is,

                                  ⇒ πR .

                                   = 3.14*18.

                                  = 56.52 cm.

                                  = 0.5652 m .

Hence, The length of the curved line of the figure​ is 0.5652 m.

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Answer 2

Answer:

The length of the curve line is 0.28 m.

Step-by-step explanation:

Length of the straight line = 18 cm

Let the radius of smaller semi circle be $r$.

And radius of the larger semicircle be $R$.

Observe that,

Length of line $AB$ = $2r+2R$ (Sum of diameters of both the semi circles)

⇒ $18 =2(r+R)$

⇒ $r+R=9$ ...... (1)

Circumference of the smaller semi circle = $\pi r$

Circumference of the larger semi circle = $\pi R$

So, length of the curve line = $\pi r+\pi R$

                                             = $\pi(r+R)$

                                             = $\frac{22}{7} (9)$

                                             = $\frac{198}{7}$ cm

                                             = $28.28$ cm

                                             = $0.28$ m.

Therefore, the length of the curve line is 0.28 m.

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