A rectangular prism has the following dimensions.

length: 8 cm

width: 13 cm

height: 10.5 cm

If all the dimensions of the prism are doubled, what will be its new surface area?

1,298 cm2
4,192 cm2
2,596 cm2
4,368 cm2

if each dimension is doubled, the surface area will be quadrupled, that is, multiplied by 4

so find the original area, multiply the answer by 4 and see if you find a match
(I see one, and it is not in the first two )

To find the new surface area of the rectangular prism when all the dimensions are doubled, we need to calculate the new length, width, and height, and then find the surface area using the formula.

Given dimensions of the rectangular prism:
Length = 8 cm
Width = 13 cm
Height = 10.5 cm

To double the dimensions, we multiply each dimension by 2:

New Length = 8 cm * 2 = 16 cm
New Width = 13 cm * 2 = 26 cm
New Height = 10.5 cm * 2 = 21 cm

To find the new surface area, we need to calculate the area of each face and sum them up.

Face 1: Area of the base = Length * Width = 16 cm * 26 cm = 416 cm^2
Face 2: Area of the opposite side = Length * Height = 16 cm * 21 cm = 336 cm^2
Face 3: Area of the other opposite side = Width * Height = 26 cm * 21 cm = 546 cm^2

Now, we add up the areas of all the faces to find the total surface area:

Surface Area = 2 * (Area of the base) + 2 * (Area of the opposite side) + 2 * (Area of the other opposite side)
Surface Area = 2 * 416 cm^2 + 2 * 336 cm^2 + 2 * 546 cm^2
Surface Area = 832 cm^2 + 672 cm^2 + 1,092 cm^2
Surface Area = 2,596 cm^2

Therefore, the new surface area of the rectangular prism, when all the dimensions are doubled, is 2,596 cm^2.

To find the new surface area of the rectangular prism after doubling all of its dimensions, we need to follow these steps:

1. Calculate the surface area of the original prism:
- The surface area of a rectangular prism is given by the formula: 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
- Plugging in the values, we get: 2(8 cm * 13 cm) + 2(8 cm * 10.5 cm) + 2(13 cm * 10.5 cm)

2. Double each dimension of the prism:
- Multiply the length, width, and height by 2. The new dimensions will be:
Length: 2 * 8 cm = 16 cm
Width: 2 * 13 cm = 26 cm
Height: 2 * 10.5 cm = 21 cm

3. Calculate the new surface area using the doubled dimensions:
- Plug in the new dimensions into the surface area formula:
2(16 cm * 26 cm) + 2(16 cm * 21 cm) + 2(26 cm * 21 cm)

4. Calculate the new surface area:
- Perform the multiplication and addition:
New surface area = 2(416 cm²) + 2(336 cm²) + 2(546 cm²) = 832 cm² + 672 cm² + 1092 cm²

Therefore, the new surface area of the rectangular prism is 2596 cm². Hence, the correct option is 2,596 cm².

6. A can of soda has dimensions as shown.

Area of top = 40 cm2