show work and find the surface area of the exhibit of a rectangular prism with the the lenth on 6 width of 8 and the hight of 14
To find the surface area of a rectangular prism, we need to calculate the areas of all six sides and then sum them up.
The formula to find the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh
Given:
Length (l) = 6
Width (w) = 8
Height (h) = 14
Substituting these values into the formula:
Surface Area = 2(6)(8) + 2(6)(14) + 2(8)(14)
= 96 + 168 + 224
= 488
Therefore, the surface area of the exhibit is 488 square units.
to create the art exihibit is by stacking 4 identicle prisms on top of eachother end to end to thier smallest faces overlap so find the art exihibit of what you just sovled bot
To find the surface area of the art exhibit, we need to calculate the surface area of each individual prism and then multiply it by 4 since there are 4 identical prisms stacked on top of each other.
We already found the surface area of one prism to be 488 square units.
So, the surface area of the art exhibit would be:
Surface Area = 4 * Surface Area of one prism
= 4 * 488
= 1952
Therefore, the surface area of the art exhibit created by stacking 4 identical prisms is 1952 square units.
findd the art exhibit not what i showed u
Apologies for the confusion. If you are looking to find the new surface area of the art exhibit created by stacking 4 identical prisms on top of each other, end to end, with their smallest faces overlapping, we need to consider the additional surface area created by the overlapping faces.
Each prism has a length (l) of 6 units, a width (w) of 8 units, and a height (h) of 14 units.
The surface area of the exhibit consists of the original surface area of the prisms plus the additional surface area created by the overlapping faces.
Original surface area of one prism = 2lw + 2lh + 2wh
= 2(6)(8) + 2(6)(14) + 2(8)(14)
= 96 + 168 + 224
= 488 square units
The additional surface area created by the overlapping faces is equal to the combined length of the overlapping faces multiplied by the height of the prisms.
Length of overlapping faces = 2 * l (since there are two of these overlapping faces)
= 2 * 6
= 12 units
Additional surface area = Length of overlapping faces * Height
= 12 * 14
= 168 square units
Total surface area of the art exhibit = Original surface area of one prism + Additional surface area
= 488 + 168
= 656 square units
Therefore, the surface area of the art exhibit created by stacking 4 identical prisms on top of each other, with their smallest faces overlapping, is 656 square units.
do the same thing but stack them sideways
If the four identical prisms are stacked sideways, with their smallest faces overlapping, let's calculate the surface area of the resulting art exhibit.
Each prism has a length (l) of 14 units, a width (w) of 8 units, and a height (h) of 6 units.
The surface area of the exhibit includes the original surface area of the prisms and the additional surface area created by the overlapping faces.
Original surface area of one prism = 2lw + 2lh + 2wh
= 2(14)(8) + 2(14)(6) + 2(8)(6)
= 224 + 168 + 96
= 488 square units
The overlapping faces occur in the width direction, and since there are two of these faces, we need to calculate the additional surface area created by the overlapping width. The additional surface area is equal to the combined width of the overlapping faces multiplied by the height of the prisms.
Width of overlapping faces = 2 * w (since there are two of these overlapping faces)
= 2 * 8
= 16 units
Additional surface area = Width of overlapping faces * Height
= 16 * 6
= 96 square units
Total surface area of the art exhibit = Original surface area of one prism + Additional surface area
= 488 + 96
= 584 square units
Therefore, the surface area of the art exhibit created by stacking 4 identical prisms sideways, with their smallest faces overlapping, is 584 square units.