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Answer :
Let's solve the problem step by step.
1) Express 1.732 in the form of [tex]\(\frac{p}{q}\)[/tex]
A decimal like 1.732 can be converted into a fraction. Initially, you can write it as [tex]\(\frac{1732}{1000}\)[/tex] because 1.732 means 1732 over 1000. Simplifying this fraction gives [tex]\(\frac{433}{250}\)[/tex]. So, the fraction form is [tex]\(\frac{433}{250}\)[/tex].
2) Find the area of a semicircle given the circumference is 176 cm
The formula for the circumference of a full circle is [tex]\(2 \pi r\)[/tex], where [tex]\(r\)[/tex] is the radius of the circle. Given the circumference is 176 cm, you can calculate the radius as follows:
[tex]\( r = \frac{176}{2\pi} \)[/tex]
Once you have the radius, the area of a full circle is given by [tex]\(\pi r^2\)[/tex]. Since we are looking for the area of a semicircle (half of a full circle), the formula becomes:
[tex]\(\text{Area of semicircle} = \frac{1}{2} \pi r^2\)[/tex]
Plug in the radius value:
[tex]\(\text{Area of semicircle} ≈ 1232.4959 \, \text{cm}^2\)[/tex]
Therefore, the area of the semicircle is approximately 1232.50 cm².
1) Express 1.732 in the form of [tex]\(\frac{p}{q}\)[/tex]
A decimal like 1.732 can be converted into a fraction. Initially, you can write it as [tex]\(\frac{1732}{1000}\)[/tex] because 1.732 means 1732 over 1000. Simplifying this fraction gives [tex]\(\frac{433}{250}\)[/tex]. So, the fraction form is [tex]\(\frac{433}{250}\)[/tex].
2) Find the area of a semicircle given the circumference is 176 cm
The formula for the circumference of a full circle is [tex]\(2 \pi r\)[/tex], where [tex]\(r\)[/tex] is the radius of the circle. Given the circumference is 176 cm, you can calculate the radius as follows:
[tex]\( r = \frac{176}{2\pi} \)[/tex]
Once you have the radius, the area of a full circle is given by [tex]\(\pi r^2\)[/tex]. Since we are looking for the area of a semicircle (half of a full circle), the formula becomes:
[tex]\(\text{Area of semicircle} = \frac{1}{2} \pi r^2\)[/tex]
Plug in the radius value:
[tex]\(\text{Area of semicircle} ≈ 1232.4959 \, \text{cm}^2\)[/tex]
Therefore, the area of the semicircle is approximately 1232.50 cm².
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