Questions about a brick: 1. State which formula (A, B, or C) below can be used to calculate the total surface area (TSA) of the given brick. The options are: A. TSA(brick) = Are... Questions about a brick: 1. State which formula (A, B, or C) below can be used to calculate the total surface area (TSA) of the given brick. The options are: 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 2. State the unit of measurement for the volume of this brick. 3. Convert the length of this brick to metres. 4. Determine the maximum number of rows of bricks that can be stacked height-wise to a height of 2100 mm.
Understand the Problem
The image presents a series of questions related to the dimensions and properties of a standard brick. These questions ask to identify the correct formula for calculating the total surface area (TSA), state the unit of measurement for volume, convert the length of the brick to meters, and determine the maximum number of brick rows that can be stacked vertically to a given height.
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: $TSA = 2(lw + lh + wh)$, where $l$ is length, $w$ is width, and $h$ is height. Option A is incorrect since it only sums the area of three faces. Option C is close to the correct formula, but it's missing the factor of 2 for each term, meaning it only calculates the area of one of each face. Option B has all the correct components.
- State the unit of measurement for volume
Since the dimensions are given in millimeters (mm), the volume will be in cubic millimeters. The unit of measurement for volume is $mm^3$ (millimeters cubed).
- Convert the length of the brick to meters
The length of the brick is 240 mm. To convert millimeters to meters, divide by 1000: $240 \div 1000 = 0.24$
Therefore, the length of the brick is 0.24 meters.
- Determine the maximum number of rows of bricks that can be stacked
The height of each brick is 70 mm. The total height available is 2100 mm. Divide the total height by the height of each brick: $2100 \div 70 = 30$
Therefore, the maximum number of rows is 30.
1.2.1: B 1.2.2: $mm^3$ 1.2.3: 0.24 m 1.2.4: 30
More Information
The total surface area (TSA) of an object represents the total area of all its surfaces. In the case of a brick, which can be modeled as a rectangular prism, the TSA is the sum of the areas of all six faces.
Tips
A common mistake is to forget to multiply each area by 2 when calculating the total surface area. This is because a rectangular prism has three pairs of identical faces. Another common mistake is using the wrong conversion factor when converting between millimeters and meters. There are 1000 millimeters in a meter, so to convert from millimeters to meters, you divide by 1000.
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