Photo AI

OAB is a sector of a circle with centre O and radius 7 cm - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 2

Question 14

OAB is a sector of a circle with centre O and radius 7 cm. The area of the sector is 40 cm². Calculate the perimeter of the sector. Give your answer correct to 3 s... show full transcript

Worked Solution & Example Answer:OAB is a sector of a circle with centre O and radius 7 cm - Edexcel - GCSE Maths - Question 14 - 2019 - Paper 2

Step 1

Calculate the size of the angle in degrees

96%

114 rated

Answer

To find the angle θ in degrees, we use the formula for the area of a sector:

$A = \frac{\theta}{360} \times \pi r^2$

Plugging in the values:

$40 = \frac{\theta}{360} \times \pi \times 7^2$

This simplifies to:

$40 = \frac{\theta}{360} \times 49\pi$ $\theta = \frac{40 \times 360}{49\pi} \approx 93.49°$

Step 2

Calculate the length of the arc

99%

104 rated

Answer

The length of the arc (L) can be calculated using the formula:

$L = \frac{\theta}{360} \times 2\pi r$

Substituting the values that we have:

$L = \frac{93.49}{360} \times 2\pi \times 7$

This gives:

$L \approx 10.87 \, \text{cm}$

Step 3

Calculate the perimeter of the sector

96%

101 rated

Answer

The perimeter (P) of the sector is the sum of the lengths of the arc and the two radii:

$P = L + 2r$

Substituting in:

$P = 10.87 + 2 \times 7 = 10.87 + 14 = 24.87 \, \text{cm}$

Rounding to three significant figures, we find:

$P \approx 24.9 \, \text{cm}$

Join the GCSE students using SimpleStudy...

97% of Students

Report Improved Results

98% of Students

Recommend to friends

100,000+

Students Supported

1 Million+

Questions answered

;