https://file.aiquickdraw.com/mathbot/file/17276788902203iesibp1.jpg

Let's solve each part of the question from the image step by step.

### Part (a):
The diagram shows a sector of a circle with radius \( r = 9 \, \text{cm} \), and the arc subtends an angle \( \theta = 100^\circ \) at the center. We need to find the area of this sector.

The formula for the area \( A \) of a sector of a circle is:

\[
A = \frac{\theta}{360^\circ} \times \pi r^2
\]

Substituting the given values:
\[
A = \frac{100^\circ}{360^\circ} \times \pi (9)^2
\]

We will calculate this value shortly.

### Part (b):
The toy consists of three parts: a cone, a cylinder, and a hemisphere. We need to identify the total surface area of the toy.

#### Step 1: Surface area of the cone
The formula for the surface area of the cone (without the base) is:

\[
A_{\text{cone}} = \pi r l
\]
where \( r = 7 \, \text{cm} \) is the radius and \( l \) is the slant height of the cone.

To find the slant height \( l \), we use the Pythagorean theorem:
\[
l = \sqrt{r^2 + h^2} = \sqrt{7^2 + 7^2} = \sqrt{98} \, \text{cm}
\]

#### Step 2: Surface area of the cylinder
The lateral surface area of the cylinder (without the top and bottom) is:

\[
A_{\text{cylinder}} = 2 \pi r h
\]
where \( r = 7 \, \text{cm} \) and \( h = 6 \, \text{cm} \).

#### Step 3: Surface area of the hemisphere
The surface area of the curved part of a hemisphere is:

\[
A_{\text{hemisphere}} = 2 \pi r^2
\]
where \( r = 7 \, \text{cm} \).

Finally, we add these areas together to get the total surface area of the toy. I will now calculate these values.### Results:

- **Part (a)**: The area of the sector \( OAB \) is approximately \( 70.69 \, \text{cm}^2 \).
  
- **Part (b)**: The total surface area of the toy (consisting of a cone, cylinder, and hemisphere) is approximately \( 789.47 \, \text{cm}^2 \).

Would you like more details or further clarifications? 

Here are five related questions:
1. How do you calculate the perimeter of the sector in part (a)?
2. What is the volume of the toy in part (b)?
3. Can you explain the difference between surface area and lateral surface area?
4. How would the surface area calculation change if the cone had a base?
5. How can we calculate the arc length for part (a)?

**Tip:** When solving geometry problems involving sectors or solids, always check whether the surface area includes the bases or not, as this can change the calculations significantly.

a) The diagram shows a sector of radius 9 cm. The arc OAB subtends an angle of 100° at the center O. Identify the area of sector OAB.
b) A toy consists of 3 solids: a cone, a cylinder, and a hemisphere. Identify the total surface area of the toy.

Learn how to calculate the area of a sector with a 9 cm radius and an angle of 100° and the total surface area of a toy consisting of a cone, a cylinder, and a hemisphere. This problem covers key geometry concepts including sector area and surface area of solids. Suitable for students in Grades 9-11.

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