The Perimeter of a semi-circle is 32.4 cm. Calculate i) radius of the semicircle ii) the area of the semicircle.
pls find the answer for this
Answers
Answer:
Given :
Perimeter of a semi- circle is 32.4 cm
To Find :
Radius of the semi- circle
Area of the semi - circle
Solution :
Let the radius of the semi- circle be ' r '
1) We have to find the radius of the semi- circle
We know that perimeter of a semi- circle is πr+2r
Thus ,
Perimeter = 32.4 cm
\sf\implies\pi\:r+2r=32.4\:cm⟹πr+2r=32.4cm
\sf\implies\:(\pi+2)r=32.4\:cm⟹(π+2)r=32.4cm
\sf\implies(\dfrac{22}{7}+2)r=32.4\:cm⟹(
7
22
+2)r=32.4cm
\sf\implies(\dfrac{36r}{7})=32.4\:cm⟹(
7
36r
)=32.4cm
\sf\implies\:r=\dfrac{32.4\times7}{36}⟹r=
36
32.4×7
\sf\implies\:r=\dfrac{226.8}{36}⟹r=
36
226.8
\sf\implies\:r=6.3\:cm⟹r=6.3cm
Hence , Radius of the semi- circle is 6.3 cm.
2) We have to find the area of the semi- circle
We know that the area of the semi- circle is πr²/2
Thus ,
{\sf\:Area}=\sf\dfrac{\pi\times\:r^{2}}{2}Area=
2
π×r
2
\sf=\dfrac{22\times(6.3)^{2}}{7\times2}=
7×2
22×(6.3)
2
\sf=\dfrac{22\times39.69}{14}=
14
22×39.69
\sf=\dfrac{873.18}{14}=
14
873.18
\sf=62.37\:cm^{2}=62.37cm
2
Hence , Area of the semi - circle is 62.37 cm².