Class9 Math New book Ex6.2 q7

Class9 Math Ex6.2 q7  Find the perimeter and area of a half-circle if its diameter is 12 cm.

Step-by-Step Solution

1. Find the Radius

Given that the diameter is 12 cm, we can find the radius (r) using:

$r = \frac{\text{diameter}}{2} = \frac{12}{2} = 6 \text{ cm}$

2. Calculate the Area

The area of a full circle is given by:-

$A = \pi r^2$

Since we need the area of a half-circle, we divide by 2:

$A_{\text{half-circle}} = \frac{1}{2} \times \pi \times 6^2$ $A = \frac{1}{2} \times \pi \times 36$ $A = 18\pi \approx 56.52 \text{ cm}^2$

3. Calculate the Perimeter

The perimeter of a half-circle includes the curved edge (half of the circumference of a full circle) and the straight-line diameter:

• The circumference of a full circle is:
  $C=2\pi r=2\times \pi \times 6=12\mathrm{\pi <span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"> </span>}$ 
• The curved part of the half-circle is half of this:
  $\frac{12\pi }{2}=6\mathrm{\pi <span\; style="font-family:\; Georgia,\; \text{'}Times\; New\; Roman\text{'},\; \text{'}Bitstream\; Charter\text{'},\; Times,\; serif;"> </span>}$ 
• Adding the straight-line diameter (12 cm):
  $P = 6\pi + 12$ 

  Implies

  $P \approx 18.84 + 12 = 30.84 \text{ cm}$

Final Answer

• Area = 56.52 cm²
• Perimeter = 30.84 cm

For detailed solution click on the following link:-

Exercise 6.2 Question 8 math class 9 Federal board

You tube channel federal board 9th

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