Let's go through each question in the image step-by-step.

Question 1

Identify the elements of the circle shown.

From the diagram:

• $O$: Center of the circle
• $A, B, C, D, E, F$: Points on the circle's circumference
• $AB$: Diameter (line passing through the center $O$)
• $FG$: Radius (half the diameter)
• $OC$: Radius
• $G$: A point on the radius, possibly where the radius meets a chord or segment.

The main elements in a circle include:

• Center
• Radius
• Diameter
• Circumference
• Chord (a line segment with endpoints on the circle)

Question 2

A wheel rotates 1000 times to cover a distance of 1320 meters. Find the radius of the wheel.

1. Calculate the circumference ($C$) of the wheel: $C = \frac{1320 \, \text{meters}}{1000} = 1.32 \, \text{meters}$

2. Use the circumference formula, $C = 2 \pi r$, to find the radius $r$: $1.32 = 2 \pi r$ $r = \frac{1.32}{2 \pi} \approx 0.21 \, \text{meters} \approx 21 \, \text{cm}$

Question 3

Calculate the perimeter of each given shape.

Part (a)

A shape with two semi-circles on either side of a rectangle:

• Rectangle length = 16 cm, width = 14 cm
• Radius of each semi-circle = $\frac{14}{2} = 7$ cm

1. Calculate the circumference of each semi-circle (half of $2 \pi r$): $\text{Perimeter of one semi-circle} = \pi \times 7 = 7\pi \approx 21.99 \, \text{cm}$

2. Add the two semi-circle perimeters and the two lengths of the rectangle: $\text{Total Perimeter} = 2 \times 16 + 2 \times 7\pi \approx 32 + 43.98 = 75.98 \, \text{cm}$

Part (b)

A quarter circle:

• Radius = 21 cm

1. Perimeter includes one-quarter of the circumference plus the two radii: $\text{Quarter circle perimeter} = \frac{1}{4} \times 2 \pi \times 21 + 2 \times 21$ $= \frac{\pi \times 21}{2} + 42 \approx 32.99 + 42 = 74.99 \, \text{cm}$

Question 4

The area of a circle is given as $28.26 \, \text{cm}^2$. Find the diameter.

1. Use the area formula, $A = \pi r^2$: $28.26 = \pi r^2$ $r^2 = \frac{28.26}{\pi} \approx 9$ $r = 3 \, \text{cm}$

2. The diameter $d = 2r = 6 \, \text{cm}$.

Question 5

A circular garden has a diameter of 28 meters. If the cost to plant grass is Rp 6,000 per square meter, calculate the total cost.

1. Find the area of the garden: $\text{Radius} = \frac{28}{2} = 14 \, \text{m}$ $\text{Area} = \pi \times 14^2 = 196\pi \approx 615.75 \, \text{m}^2$

2. Calculate the total cost: $\text{Total Cost} = 615.75 \times 6000 = 3,694,500 \, \text{Rp}$

Would you like further details on any of these answers? Here are five related questions:

1. How do you calculate the circumference of a circle with different values for radius?
2. Can the formula for area be used to solve problems involving arcs or sectors?
3. How would the cost change if the radius of the garden were doubled?
4. What happens to the diameter if the area of the circle doubles?
5. How would you calculate the perimeter of an irregular shape that includes arcs and straight edges?

Tip: Remember that understanding the basic formulas for circles (like area and circumference) makes it easier to handle complex shapes that include arcs or semi-circles.