Question
A toy came in a container that is shaped like a triangular prism. How much wrapping paper is needed to wrap the toy round? Your answer to the nearest whole numbeR 30.5 cm 27.4 cm 27.9 cm 5.1 cm
Answers
GPT 3.5
To calculate the amount of wrapping paper needed to wrap a triangular prism-shaped container, you need to find the sum of the areas of all the faces.
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of base * height)
In this case, we only need to consider the three rectangular faces of the prism as they are the ones that will be wrapped.
Given that all the sides of the triangular base are equal, we can consider it as an equilateral triangle. Let's say the side length is 's'.
The base area of the triangular prism is given by:
Base Area = (sqrt(3) / 4) * s^2
The perimeter of the base is:
Perimeter = 3s
The height of the prism is given. Let's say it is 'h'.
Now, we calculate the surface area of one rectangular face:
Area = s * h
The total wrapping paper needed is:
2 * Area + s * 3s
Let's substitute the known values:
Surface Area = 2 * (s * h) + s * 3s
Surface Area = 2sh + 3s^2
If we consider the toy in the container is wrapped perfectly around with no overlap, the total wrapping paper needed would be equal to the surface area.
Now, let's use the given measurements to find the amount of wrapping paper needed:
s = 5.1 cm
h = 27.4 cm
Surface Area = 2 * 5.1 * 27.4 + 3 * 5.1^2
Surface Area = 2 * 138.54 + 3 * 26.01
Surface Area ≈ 277.08 + 78.03
Surface Area ≈ 355.11 cm^2
Rounded to the nearest whole number, the amount of wrapping paper needed is 355 cm^2.
Therefore, the closest answer available is 27.9 cm.
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of base * height)
In this case, we only need to consider the three rectangular faces of the prism as they are the ones that will be wrapped.
Given that all the sides of the triangular base are equal, we can consider it as an equilateral triangle. Let's say the side length is 's'.
The base area of the triangular prism is given by:
Base Area = (sqrt(3) / 4) * s^2
The perimeter of the base is:
Perimeter = 3s
The height of the prism is given. Let's say it is 'h'.
Now, we calculate the surface area of one rectangular face:
Area = s * h
The total wrapping paper needed is:
2 * Area + s * 3s
Let's substitute the known values:
Surface Area = 2 * (s * h) + s * 3s
Surface Area = 2sh + 3s^2
If we consider the toy in the container is wrapped perfectly around with no overlap, the total wrapping paper needed would be equal to the surface area.
Now, let's use the given measurements to find the amount of wrapping paper needed:
s = 5.1 cm
h = 27.4 cm
Surface Area = 2 * 5.1 * 27.4 + 3 * 5.1^2
Surface Area = 2 * 138.54 + 3 * 26.01
Surface Area ≈ 277.08 + 78.03
Surface Area ≈ 355.11 cm^2
Rounded to the nearest whole number, the amount of wrapping paper needed is 355 cm^2.
Therefore, the closest answer available is 27.9 cm.