Advanced-WS-G8- Practice Problems on Surface Area of Cubes and ... - Free Printable

Let's solve each problem step by step.

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Problem 1:

A cube with an edge of 7 cm and a cuboid measuring 7 cm × 4 cm × 8 cm are kept on a table. Which shape has more volume?

#### Step 1: Volume of the cube
Formula for volume of a cube:
$$
V = \text{edge}^3
$$
$$
V = 7^3 = 343 \text{ cm}^3
$$

#### Step 2: Volume of the cuboid
Formula for volume of a cuboid:
$$
V = \text{length} \times \text{breadth} \times \text{height}
$$
$$
V = 7 \times 4 \times 8 = 224 \text{ cm}^3
$$

#### Compare:
- Cube: 343 cm³
- Cuboid: 224 cm³

✔ Answer: The cube has more volume.

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Problem 2:

A cuboid is 9 cm long, 5 cm broad, and 4 cm high and a cube has an edge of 5 cm. Which one has greater volume?

#### Step 1: Volume of the cuboid
$$
V = 9 \times 5 \times 4 = 180 \text{ cm}^3
$$

#### Step 2: Volume of the cube
$$
V = 5^3 = 125 \text{ cm}^3
$$

#### Compare:
- Cuboid: 180 cm³
- Cube: 125 cm³

✔ Answer: The cuboid has greater volume.

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Problem 3:

What is the volume of a brick of ice-cream with length 25 cm, breadth 10 cm, and height 8 cm?

Use the formula for volume of a cuboid:
$$
V = 25 \times 10 \times 8 = 2000 \text{ cm}^3
$$

✔ Answer: The volume is 2000 cm³.

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Problem 4:

A brick measures 15 cm in length, 8 cm in breadth, and 5 cm in height. How many bricks will be used to make a wall of length 15 m, breadth 10 m, and height 8 metres?

#### Step 1: Convert wall dimensions to centimeters
Since the brick dimensions are in cm, convert meters to cm:
- 15 m = 1500 cm
- 10 m = 1000 cm
- 8 m = 800 cm

#### Step 2: Volume of the wall
$$
V_{\text{wall}} = 1500 \times 1000 \times 800 = 1,200,000,000 \text{ cm}^3
$$

#### Step 3: Volume of one brick
$$
V_{\text{brick}} = 15 \times 8 \times 5 = 600 \text{ cm}^3
$$

#### Step 4: Number of bricks needed
$$
\text{Number of bricks} = \frac{V_{\text{wall}}}{V_{\text{brick}}} = \frac{1,200,000,000}{600} = 2,000,000
$$

✔ Answer: 2,000,000 bricks are needed.

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✔ Final Answers Summary:

1. Cube has more volume.
2. Cuboid has greater volume.
3. Volume of ice-cream brick = 2000 cm³
4. Number of bricks needed = 2,000,000

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