Math / Geometry

Question(b) Rajah di bawah menunjukkan sebuah bulatan dengan pusat $O$ dan jejari $j \mathrm{~cm}$ . $L$ adalah luas sektor minor bagi bulatan tersebut. The diagram below shows a circle with centre $O$ and radius of $j \mathrm{~cm}, L$ is the area of minor sector of the circle.
Berdasarkan rajah tersebut, lengkapkan jadual di ruang jawapan dengan menggunakan pilihan jawapan di bawah. Based on the diagram, complete the table in the ansiver space using the options below. (Guna / use $\pi=\frac{22}{7}$ ) \begin{tabular}{|l|l|l|l|} \hline 12 & 14 & 130 & 150 \\ \hline \end{tabular}
Jawapan / Answer. \begin{tabular}{|c|c|c|} \hline $\theta^{\circ}$ & $j \mathrm{~cm}$ & $L \mathrm{~cm}^{2}$ \\ \hline 120 & & 150.85 \\ \hline & 7 & 64.17 \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We need to find the radius and angle of a circle sector, given its area and some other information. Watch out! Don't mix up the radius and the angle, and make sure to use the correct formula for the area of a sector.
Also, remember they've asked us to use a specific value for $\pi$ .

STEP 2

1. Find the radius
2. Find the angle

STEP 3

The area $L$ of a sector of a circle with radius $j$ and angle $\theta$ (in degrees) is given by $L = \frac{\theta}{360} \cdot \pi \cdot j^2$ .
Remember, this formula comes from the fact that the sector is a fraction of the whole circle.
The fraction is represented by $\frac{\theta}{360}$ .

STEP 4

We are given $L = 64.17 \text{ cm}^2$ , $\pi = \frac{22}{7}$ , and $j = 7 \text{ cm}$ .
We're asked to find $\theta$ .
Let's plug in the values we know: $64.17 = \frac{\theta}{360} \cdot \frac{22}{7} \cdot 7^2$

STEP 5

Let's simplify and solve for $\theta$ : $64.17 = \frac{\theta}{360} \cdot \frac{22}{7} \cdot 49$ $64.17 = \frac{\theta}{360} \cdot 22 \cdot 7$ $64.17 = \frac{\theta}{360} \cdot 154$ Now, multiply both sides by 360: $64.17 \cdot 360 = \theta \cdot 154$ $23101.2 = \theta \cdot 154$ Finally, divide both sides by 154 to isolate $\theta$ : $\theta = \frac{23101.2}{154}$ $\theta = 150$ So, the angle is $\theta = 150^\circ$ .

STEP 6

We'll use the same formula as before: $L = \frac{\theta}{360} \cdot \pi \cdot j^2$ .

STEP 7

This time, we have $L = 150.85 \text{ cm}^2$ , $\pi = \frac{22}{7}$ , and $\theta = 120^\circ$ .
We need to find $j$ .
Let's plug in what we know: $150.85 = \frac{120}{360} \cdot \frac{22}{7} \cdot j^2$

STEP 8

Let's simplify and solve for $j$ : $150.85 = \frac{1}{3} \cdot \frac{22}{7} \cdot j^2$ Multiply both sides by 3: $452.55 = \frac{22}{7} \cdot j^2$ Now, multiply both sides by 7: $3167.85 = 22 \cdot j^2$ Divide both sides by 22: $j^2 = \frac{3167.85}{22}$ $j^2 = 144$ Take the square root of both sides (remembering that the radius must be positive): $j = \sqrt{144}$ $j = 12$ So, the radius is $j = 12 \text{ cm}$ .

STEP 9

The missing radius is $12 \text{ cm}$ and the missing angle is $150^\circ$ .

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Studdy Solution

STEP 1

STEP 2

1. Find the radius
2. Find the angle

STEP 3

The area $L$ of a sector of a circle with radius $j$ and angle $\theta$ (in degrees) is given by $L = \frac{\theta}{360} \cdot \pi \cdot j^2$ .
Remember, this formula comes from the fact that the sector is a fraction of the whole circle.
The fraction is represented by $\frac{\theta}{360}$ .

STEP 4

We are given $L = 64.17 \text{ cm}^2$ , $\pi = \frac{22}{7}$ , and $j = 7 \text{ cm}$ .
We're asked to find $\theta$ .
Let's plug in the values we know: $64.17 = \frac{\theta}{360} \cdot \frac{22}{7} \cdot 7^2$

STEP 5

STEP 6

We'll use the same formula as before: $L = \frac{\theta}{360} \cdot \pi \cdot j^2$ .

STEP 7

This time, we have $L = 150.85 \text{ cm}^2$ , $\pi = \frac{22}{7}$ , and $\theta = 120^\circ$ .
We need to find $j$ .
Let's plug in what we know: $150.85 = \frac{120}{360} \cdot \frac{22}{7} \cdot j^2$

STEP 8

STEP 9

The missing radius is $12 \text{ cm}$ and the missing angle is $150^\circ$ .

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Studdy Solution

STEP 1

STEP 2

1. Find the radius2. Find the angle

STEP 3

STEP 4

We are given L=64.17 cm2L = 64.17 \text{ cm}^2L=64.17 cm2, π=227\pi = \frac{22}{7}π=722​, and j=7 cmj = 7 \text{ cm}j=7 cm.We're asked to find θ\thetaθ.Let's plug in the values we know: 64.17=θ360⋅227⋅7264.17 = \frac{\theta}{360} \cdot \frac{22}{7} \cdot 7^264.17=360θ​⋅722​⋅72

STEP 5

STEP 6

We'll use the same formula as before: L=θ360⋅π⋅j2L = \frac{\theta}{360} \cdot \pi \cdot j^2L=360θ​⋅π⋅j2.

STEP 7

This time, we have L=150.85 cm2L = 150.85 \text{ cm}^2L=150.85 cm2, π=227\pi = \frac{22}{7}π=722​, and θ=120∘\theta = 120^\circθ=120∘.We need to find jjj.Let's plug in what we know: 150.85=120360⋅227⋅j2150.85 = \frac{120}{360} \cdot \frac{22}{7} \cdot j^2150.85=360120​⋅722​⋅j2

STEP 8

STEP 9

The missing **radius** is 12 cm12 \text{ cm}12 cm and the missing **angle** is 150∘150^\circ150∘.

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1. Find the radius
2. Find the angle

We are given $L = 64.17 \text{ cm}^2$ , $\pi = \frac{22}{7}$ , and $j = 7 \text{ cm}$ .
We're asked to find $\theta$ .
Let's plug in the values we know: $64.17 = \frac{\theta}{360} \cdot \frac{22}{7} \cdot 7^2$

We'll use the same formula as before: $L = \frac{\theta}{360} \cdot \pi \cdot j^2$ .

This time, we have $L = 150.85 \text{ cm}^2$ , $\pi = \frac{22}{7}$ , and $\theta = 120^\circ$ .
We need to find $j$ .
Let's plug in what we know: $150.85 = \frac{120}{360} \cdot \frac{22}{7} \cdot j^2$

The missing radius is $12 \text{ cm}$ and the missing angle is $150^\circ$ .