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QuestionFind the surface area of a similar rectangular solid with width 10, given the original has dimensions 16, 20, and area 4480.

Studdy Solution

STEP 1

Assumptions1. The length of the first rectangular solid is16. The width of the first rectangular solid is203. The total surface area of the first rectangular solid is44804. The width of the second rectangular solid is105. The second rectangular solid is similar to the first one, which means the ratio of corresponding sides is constant

STEP 2

First, we need to find the ratio of the widths of the two solids. This ratio will be the same for all corresponding sides and surface areas of the two solids.
Ratio=Width of second solid/Width of first solidRatio = Width\, of\, second\, solid / Width\, of\, first\, solid

STEP 3

Now, plug in the given values for the widths of the two solids to calculate the ratio.
Ratio=10/20Ratio =10 /20

STEP 4

Calculate the ratio.
Ratio=10/20=0.Ratio =10 /20 =0.

STEP 5

The surface area of a similar figure changes by the square of the scale factor. So, we need to square the ratio to find the ratio of the surface areas of the two solids.
Surface area ratio=(Ratio)2Surface\, area\, ratio = (Ratio)^2

STEP 6

Now, plug in the calculated ratio to find the surface area ratio.
Surface area ratio=(0.5)2Surface\, area\, ratio = (0.5)^2

STEP 7

Calculate the surface area ratio.
Surface area ratio=(0.5)2=0.25Surface\, area\, ratio = (0.5)^2 =0.25

STEP 8

Now that we have the surface area ratio, we can find the surface area of the second solid by multiplying the surface area of the first solid by the surface area ratio.
Surface area of second solid=Surface area of first solidtimesSurface area ratioSurface\, area\, of\, second\, solid = Surface\, area\, of\, first\, solid \\times Surface\, area\, ratio

STEP 9

Now, plug in the given value for the surface area of the first solid and the calculated surface area ratio to find the surface area of the second solid.
Surface area of second solid=448times.25Surface\, area\, of\, second\, solid =448 \\times.25

STEP 10

Calculate the surface area of the second solid.
Surface area of second solid=4480times0.25=1120Surface\, area\, of\, second\, solid =4480 \\times0.25 =1120The total surface area of the similar rectangular solid with a width of10 is1120.

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