Question

Wedge of cheese shaped line a prism. 5 by 12 by 9 by 13cm. How much plastic wrap is needed

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the surface area of the prism-shaped cheese wedge, we need to calculate the area of each of the five faces of the prism and then add them together.

The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
where l = length, w = width, and h = height.

Given dimensions:
Length (l) = 12cm
Width (w) = 9cm
Height (h) = 5cm
Slant height of the wedge = 13cm

Now we calculate the surface areas of each face of the cheese wedge:
1. Top face: l x w = 12cm x 9cm = 108 cm^2
2. Bottom face: l x w = 12cm x 9cm = 108 cm^2
3. Front face: w x h = 9cm x 5cm = 45 cm^2
4. Back face: w x h = 9cm x 5cm = 45 cm^2
5. Slant face: triangle area = 1/2 x base x height = 1/2 x 12cm x 5cm = 30 cm^2

Now, let's calculate the total surface area:
Surface Area = 2(108) + 2(45) + 2(30) = 216 + 90 + 60 = 366 cm^2

Therefore, 366 square centimeters of plastic wrap will be needed to cover the wedge of cheese.

Answer 2

no

Answer 3

[AI-generated answer — Bot GPT 3.5]

I apologize for the mistake in my previous calculation. Let's correct it.

To find the total surface area of the prism-shaped cheese wedge, we need to calculate the area of each face and slanted sides.

The formula for the surface area of a prism is:
Surface Area = 2lw + 2lh + wh
where l = length, w = width, and h = height.

Given dimensions:
Length (l) = 12cm
Width (w) = 9cm
Height (h) = 5cm
Slant side height = 13cm

Now we calculate the surface areas of each face and slanted sides:
1. Top face: l x w = 12cm x 9cm = 108 cm^2
2. Bottom face: l x w = 12cm x 9cm = 108 cm^2
3. Front face: w x h = 9cm x 5cm = 45 cm^2
4. Back face: w x h = 9cm x 5cm = 45 cm^2
5. Slanted sides (x 2): Area of trapezoid = 1/2 (w1 + w2) x slant side height = 1/2(9 + 12) x 13 = 105 cm^2

Now, let's calculate the total surface area:
Surface Area = 2(108) + 2(45) + 105 = 216 + 90 + 105 = 411 cm^2

Therefore, 411 square centimeters of plastic wrap will be needed to cover the wedge of cheese.