Math Problem Statement

tolong jawab diketahui ditanya dijawab yaaa

tolong jawab diketahui ditanya dijawab yaaa

Solution

Sure, I’ll help solve the problems from the uploaded images using the structure "diketahui" (given), "ditanya" (asked), and "jawab" (solution). Let's go through each visible question.


Image 1

Problem 8:

  • Diketahui:
    • Sudut pusat lingkaran = 6060^\circ
    • Jari-jari lingkaran = 21 cm
  • Ditanya: Panjang busur lingkaran
  • Jawab:
    • Rumus panjang busur lingkaran: L=θ360×2πrL = \frac{\theta}{360^\circ} \times 2 \pi r
    • Substitute values: L=60360×2π×21L = \frac{60^\circ}{360^\circ} \times 2 \pi \times 21
    • Simplify: L=16×2π×21=22 cmL = \frac{1}{6} \times 2 \pi \times 21 = 22 \text{ cm}
    • Jawaban: E. 22 cm

Problem 9:

  • Diketahui:
    • Jari-jari lingkaran = 3 m
  • Ditanya: Panjang garis putih yang membentuk lingkaran (keliling)
  • Jawab:
    • Rumus keliling lingkaran: K=2πrK = 2 \pi r
    • Substitute values: K=2π×3=6π18.8 mK = 2 \pi \times 3 = 6 \pi \approx 18.8 \text{ m}
    • Jawaban: D. 18.8 m

Problem 10:

  • Diketahui:
    • Sudut pusat PTR=120\angle PTR = 120^\circ
  • Ditanya: Nilai β\beta
  • Jawab:
    • Karena sudut pusat adalah 120120^\circ, maka sudut keliling yang bersesuaian (β\beta) adalah setengah dari sudut pusat.
    • β=1202=60\beta = \frac{120^\circ}{2} = 60^\circ
    • Jawaban: E. 60°

Image 2

Problem 4:

  • Diketahui:
    • Jari-jari lingkaran = 21 cm
    • Sudut pusat ACB=120\angle ACB = 120^\circ
  • Ditanya: Panjang busur ACB\text{ACB}
  • Jawab:
    • Rumus panjang busur: L=θ360×2πrL = \frac{\theta}{360^\circ} \times 2 \pi r
    • Substitute values: L=120360×2π×21L = \frac{120^\circ}{360^\circ} \times 2 \pi \times 21
    • Simplify: L=13×2π×21=44 cmL = \frac{1}{3} \times 2 \pi \times 21 = 44 \text{ cm}
    • Jawaban: B. 44 cm

Problem 5:

  • Diketahui:
    • Jari-jari lingkaran M=7M = 7 cm
    • Panjang busur PQ=9.6PQ = 9.6 cm
  • Ditanya: Besar sudut PMQPMQ
  • Jawab:
    • Rumus panjang busur lingkaran: L=θ360×2πrL = \frac{\theta}{360^\circ} \times 2 \pi r
    • Substitute values and solve for θ\theta: 9.6=θ360×2π×79.6 = \frac{\theta}{360^\circ} \times 2 \pi \times 7
    • Simplify: θ=9.6×3602π×778\theta = \frac{9.6 \times 360^\circ}{2 \pi \times 7} \approx 78^\circ
    • Jawaban: D. 80°

If you need further assistance or if you have questions about other specific problems on the page, please let me know. Here are some related questions for practice:

  1. What would be the length of an arc if the radius is doubled but the central angle remains the same?
  2. How do you calculate the circumference of a circle with a radius of 10 cm?
  3. If the radius is halved, how does the length of the arc change for a fixed angle?
  4. What formula relates the area of a sector to its central angle?
  5. How would you find the angle if only the arc length and radius are given?

Tip: Remember, when calculating the length of an arc, it’s helpful to convert the angle to radians for simpler calculations in more advanced math contexts.

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Math Problem Analysis

Mathematical Concepts

Geometry
Circle
Arc Length
Circumference
Angle Measures

Formulas

Arc length formula: L = (θ / 360°) * 2πr
Circumference formula: C = 2πr

Theorems

Central Angle Theorem: the measure of an inscribed angle is half the measure of its intercepted arc or central angle.

Suitable Grade Level

Grade 8