Question

1. use this diagram to help you write a formula for the relationship between the radius and the diameter of a circle.

• point c is the centre of the circle.
• ac and bc are radii of the circle.
• ab is a diameter of the circle.

\\(ac + bc = ab\\). the length of this diameter must be ______ the length of each radius.

so, \\(d = \\) ______ \\(r\\).

1. the distance from the centre of a portable pool to its edge is \\(2.5\text{ m}\\).

a) what is the radius of the solar blanket that just covers the pool? ______
b) what is the diameter of the solar blanket? ______

1. the top part of this window is a semicircle. determine the height of the window.

height of rectangular part of window = ______
height of the semicircle = ______
height of window = ____ + ____
= ______

Explanation:

🆕 New Concept Discovered: Circle Geometry (Radius and Diameter)
The relationship between a circle's radius (distance from center to edge) and diameter (distance across through the center).

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Step 1: Solve Question 8

We are given that \( AC \) and \( BC \) are radii (\( r \)) of the circle, and \( AB \) is the diameter (\( d \)).
Since \( AC + BC = AB \), we substitute the radius \( r \) for both \( AC \) and \( BC \):

$$ r + r = d $$

$$ 2r = d $$

This means the length of the diameter is twice (or double) the length of each radius.

• First blank: twice (or double)
• Second blank: 2

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Step 2: Solve Question 9

The distance from the center of a circular pool to its edge is defined as its radius. We are given this distance is \( 2.5\text{ m} \).

• a) Radius of the solar blanket:

Since the blanket just covers the pool, its radius is equal to the pool's radius:

$$ r = 2.5\text{ m} $$

• b) Diameter of the solar blanket:

The diameter is twice the radius:

$$ d = 2 \times r = 2 \times 2.5\text{ m} = 5\text{ m} $$

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Step 3: Solve Question 10

We need to find the total height of the window, which consists of a rectangular bottom and a semicircular top.

1. Height of rectangular part of window:

Looking at the diagram, the height of the rectangular section is directly labeled:

$$ 90\text{ cm} $$

1. Height of the semicircle:

The width of the window is \( 120\text{ cm} \), which is the diameter (\( d \)) of the semicircle at the top. The height of a semicircle from its base to its highest point is equal to its radius (\( r \)):

$$ r = \frac{d}{2} = \frac{120\text{ cm}}{2} = 60\text{ cm} $$

1. Height of window:

Add the height of the rectangular part and the height of the semicircle:

$$ \text{Total Height} = 90\text{ cm} + 60\text{ cm} = 150\text{ cm} $$

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Answer:

Question 8:

• The length of this diameter must be twice (or double) the length of each radius.
• So, \( d = \) 2 \( r \).

Question 9:

• a) \( 2.5\text{ m} \)
• b) \( 5\text{ m} \)

Question 10:

• Height of rectangular part of window = \( 90\text{ cm} \)
• Height of the semicircle = \( 60\text{ cm} \)
• Height of window = \( 90\text{ cm} \) + \( 60\text{ cm} \) = \( 150\text{ cm} \)