Jenny has found the total surface area and the lateral surface area of a prism, but she can’t remember which is which. She got answers of 144 in.2 and 304 in.2 . How would you distinguish which answer is lateral surface area and which is total surface area?
To distinguish between the total surface area and the lateral surface area, we need to compare the given values to the known formulas for these areas.
The total surface area of a prism is calculated by adding the areas of all the faces of the prism. It includes both the lateral surface area (the sum of all the faces excluding the top and bottom) and the base areas.
The lateral surface area of a prism, on the other hand, only considers the combined area of the side faces, excluding the base areas.
Given that Jenny's answers are 144 in.2 and 304 in.2, we can determine which is which by comparing them to the known formulas.
If the smaller answer (144 in.2) represents the lateral surface area, then the larger answer (304 in.2) must be the total surface area because it includes the lateral surface area as well as the base areas.
Conversely, if the larger answer (304 in.2) represents the lateral surface area, then the smaller answer (144 in.2) must be the total surface area because it includes the lateral surface area as well as the base areas.
Therefore, without further information, it is not possible to determine which answer corresponds to the lateral surface area and which corresponds to the total surface area.
A. the lateral surface area is 304 in.^2 and the total surface area is 144 in.^2. the greater area is the lateral surface area.
B.The lateral surface area is 144 in.^2, and the total surface area is 304 in.^2 the area that is less is the lateral surface area
C. There is not enough information given to distinguish lateral surface area from total surface area.
D. The two areas should be the same, so Jenny should recaululate
To distinguish between the total surface area and the lateral surface area, we need to compare the given values to the known formulas for these areas.
The lateral surface area of a prism is the sum of all the faces excluding the top and bottom faces. It does not include the base areas.
The total surface area of a prism is the sum of all the faces of the prism, including the top and bottom faces.
Given that Jenny's answers are 144 in.^2 and 304 in.^2, we can determine which is which by comparing them to the known formulas.
Option B states that the lateral surface area is 144 in.^2 and the total surface area is 304 in.^2. However, this contradicts the known formulas since the lateral surface area should always be less than or equal to the total surface area. Therefore, Option B is incorrect.
Option A states that the lateral surface area is 304 in.^2 and the total surface area is 144 in.^2. This aligns with the known formulas since the lateral surface area can be greater than the total surface area when the bases have a small area compared to the side faces. This option correctly identifies the lateral surface area as the greater area. Therefore, Option A is the correct answer.
Option C suggests that there is not enough information given to distinguish the lateral surface area from the total surface area. However, using the known formulas, we can distinguish the two based on their values. Therefore, Option C is incorrect.
Option D suggests that the two areas should be the same and Jenny should recalculate. However, there is no rule stating that the lateral surface area and the total surface area should be the same. Therefore, Option D is incorrect.
In conclusion, the correct answer is Option A: The lateral surface area is 304 in.^2 and the total surface area is 144 in.^2. The greater area is the lateral surface area.