Surface area calculation worksheet for cubes and cuboids.

Here are the step-by-step solutions for each question.

Question 1: Surface Area of a Cube

Step 1: Identify the shape and dimensions.
The shape is a cube with a side length of 6 cm. A cube has 6 identical square faces.

Step 2: Calculate the area of one face.
Area of one face = side × side
$$6 \text{ cm} \times 6 \text{ cm} = 36 \text{ cm}^2$$

Step 3: Calculate the total surface area.
Since there are 6 faces, multiply the area of one face by 6.
$$36 \text{ cm}^2 \times 6 = 216 \text{ cm}^2$$

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Question 2: Surface Area of a Cuboid

Step 1: Identify the dimensions.
Length ($l$) = 3 cm
Width ($w$) = 2 cm
Height ($h$) = 6 cm

Step 2: Use the formula for the surface area of a cuboid.
Formula: $2(lw + lh + wh)$

* Area of front and back faces ($l \times h$): $3 \times 6 = 18$
* Area of top and bottom faces ($l \times w$): $3 \times 2 = 6$
* Area of side faces ($w \times h$): $2 \times 6 = 12$

Step 3: Add them up and multiply by 2.
Sum inside brackets: $18 + 6 + 12 = 36$
Total Surface Area: $36 \times 2 = 72 \text{ cm}^2$

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Question 3: Surface Area of a Large Cuboid

Step 1: Identify the dimensions.
Length = 3 m
Breadth (width) = 10 m
Height = 1 m

Step 2: Calculate the area of the pairs of faces.
* Top and Bottom ($3 \text{ m} \times 10 \text{ m}$): $30 \text{ m}^2$ each. Total = $60 \text{ m}^2$.
* Front and Back ($3 \text{ m} \times 1 \text{ m}$): $3 \text{ m}^2$ each. Total = $6 \text{ m}^2$.
* Sides ($10 \text{ m} \times 1 \text{ m}$): $10 \text{ m}^2$ each. Total = $20 \text{ m}^2$.

Step 3: Add all areas together.
$$60 + 6 + 20 = 86 \text{ m}^2$$

*(Note: The worksheet asks for the answer in $\text{cm}^2$, but the measurements are given in meters. Based on standard math problems, the unit label on the line is likely a typo, and the answer should be in square meters to match the question's data.)*

Final Answer:
1. Answer : 216 cm²
2. Answer : 72 cm²
3. Answer : 86 cm²