The problem in the image asks to calculate the surface area of a composite shape, which seems to be a cylinder with two hemispherical ends. It also specifies to use $\pi = \frac{22}{7}$.

Given dimensions:

• Length of the cylinder (without hemispheres) = 35 cm
• Radius of the base (and hemisphere) = 7 cm

Step-by-Step Solution:

1. Surface Area of the Cylinder (without the hemispheres): The surface area of a cylinder (lateral area) is given by: $\text{Lateral Area of Cylinder} = 2 \pi r h$ where:

   • $r = 7 \, \text{cm}$ (radius),
   • $h = 35 \, \text{cm}$ (height of the cylindrical part).

   Substituting the values: $\text{Lateral Area} = 2 \times \frac{22}{7} \times 7 \times 35 = 2 \times 22 \times 35 = 1540 \, \text{cm}^2$

2. Surface Area of the Two Hemispheres: The total surface area of two hemispheres is the same as the surface area of a full sphere. The surface area of a sphere is given by: $\text{Surface Area of Sphere} = 4 \pi r^2$ where $r = 7 \, \text{cm}$.

   Substituting the values: $\text{Surface Area of Hemispheres} = 4 \times \frac{22}{7} \times 7^2 = 4 \times \frac{22}{7} \times 49 = 4 \times 154 = 616 \, \text{cm}^2$

3. Total Surface Area: The total surface area is the sum of the lateral area of the cylinder and the surface area of the two hemispheres: $\text{Total Surface Area} = 1540 + 616 = 2156 \, \text{cm}^2$

Final Answer:

The surface area of the composite shape is 2156 cm².

Would you like further details on this calculation or explanations? Here are some related questions for practice:

1. How do you calculate the volume of a cylinder with hemispherical ends?
2. What is the formula for the volume of a hemisphere?
3. How does changing the radius affect the surface area of a cylinder?
4. What is the difference between lateral and total surface area in a cylinder?
5. Can you apply this formula to other composite shapes, like a cone?

Tip: Always double-check the units and dimensions when working with surface area to avoid errors in calculations!