1. The sketch below shows a standard brick, with dimensions, used in South Africa. Use the information above to answer the questions that follow. 2. State which formula (A, B or C)... 1. The sketch below shows a standard brick, with dimensions, used in South Africa. Use the information above to answer the questions that follow. 2. State which formula (A, B or C) below can be used to calculate the total surface area (TSA) of the given brick. A. TSA(brick) = Area of front side + Area of right-hand side + Area of top B. TSA(brick) = (2 x 240 x 70 + 2 x 240 x 112 + 2 x 112 x 70) mm² C. TSA(brick) = (240 x 70 + 240 x 112 + 112 x 70) mm² 3. State the unit of measurement for the volume of this brick. 4. Convert the length of this brick to metres. 5. Determine the maximum number of rows of bricks that can be stacked height-wise to a height of 2100 mm.
Understand the Problem
The question provides a diagram of a standard brick with its dimensions (height, width, and length). It asks you to use this information to answer four questions: 1) Select the correct formula for calculating the total surface area (TSA) of the brick from three options. 2) State the unit of measurement for volume. 3) Convert the length of the brick from millimeters to meters. 4) Determine the maximum number of rows of bricks that can be stacked to reach a height of 2100 mm.
Answer
1.2.1: B 1.2.2: $mm^3$ 1.2.3: 0.24 m 1.2.4: 30
Answer for screen readers
1.2.1: B 1.2.2: $mm^3$ 1.2.3: 0.24 m 1.2.4: 30
Steps to Solve
- Identify the correct formula for the total surface area (TSA)
The total surface area of a rectangular prism (like a brick) is given by the formula:
$TSA = 2lw + 2lh + 2wh$, where $l$ is length, $w$ is width, and $h$ is height.
Formula A is incorrect because it only considers one of each of the faces and omits that each face has a matching face on the opposite side of the brick. Formula B correctly uses the dimensions given to express the total surface area. Formula C, like A, omits that each face has a matching face on the opposite side of the brick.
- State the unit of measurement for volume
Volume is measured in cubic units. Since the dimensions are given in millimeters (mm), the volume will be in cubic millimeters ($mm^3$).
- Convert the length of the brick to meters
Given that the length of the brick is 240 mm, and knowing that 1 meter = 1000 millimeters, we can convert the length to meters by dividing by 1000:
$240 \text{ mm} \div 1000 = 0.24 \text{ m}$
- Determine the maximum number of rows of bricks
The height of each brick is 70 mm. The total height to be reached is 2100 mm. To find the maximum number of rows, divide the total height by the height of one brick:
$2100 \text{ mm} \div 70 \text{ mm} = 30$
1.2.1: B 1.2.2: $mm^3$ 1.2.3: 0.24 m 1.2.4: 30
More Information
The formula for the total surface area of a rectangular prism is $2lw + 2lh + 2wh$ Volume is always measured in cubic units, for example $m^3, cm^3, mm^3$ and so on. To convert from millimeters to meters, divide by 1000.
Tips
A common mistake is forgetting to include the "2" in the surface area formula, which accounts for all faces of the brick (top/bottom, left/right, front/back). Also, students might incorrectly divide instead of multiply when converting between units, or vice versa. A similar major mistake in 1.2.4 would be multiplying instead of dividing, ending up with a much larger, and therefore incorrect, number of rows.
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