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The volumes of two similar figures are 512 mm3 and 3375mm3. If the surface area of the smaller figure is 128mm2. What is the surface area of the larger figure?
450 mm2
Ratio of areas is the square of the ratio of lengths.
Ratio of volumes is the cube of the ratios of lengths.
If the volumes are in the ratio of 512 to 3375, then the lengths are in the ratio of:
3√512 : 3√3375 = 8 : 15
⇒ ratios of areas:
82 : 152 = 64 : 225
⇒ as smaller has surface area of 128 mm2, the larger has:
surface_area = (128 ÷ 64) x 225 mm2
= 450 mm2
What else can I help you with?
Do figures with the same volume always have the same surface area?
figures with the same volume does not have the same surface area.
The volumes of two similar figures are 343 mm cubed and 512 mm cubed If the surface area of the larger figure is 192 mm squared what is the surface area of the smaller figure?
If the volumes are 343 mm3 and 512 mm3 then these represent a three dimensional object. The equivalent ratio of a single dimension is ³√343 : ³√512 = 7 : 8. Areas are proportional to the square of the single dimension, namely 72 : 82 = 49 : 64. Let A be the surface area of the smaller figure. As the areas are proportional then A/192 = 49/64 Therefore A = 192 x 49/64 = 147 mm2.
What is the difference between lateral area and surface area?
the formulas for lateral area dont include the figures bases. surface area does.
What is the surface area of an octagon?
First of all, you did not provide measurements for the octagon. Second, surface area is meant for three-dimensional figures. Octagons are two-dimensional.
How can you use area formulas for 2-D figures to derive formulas for surface areas of 3-D figures?
-1
The surface area of two similar figures are 36in and 49in if the volume of the smaller figure is 648 in what is the volume of the larger figure?
v
If volume of two similar figures are 729 mm cubed plus 2744 mm cubed if the surface area of the larger figure is 392 mm squared what is the surface area of the smaller figure?
To find the surface area of the smaller figure, we can use the relationship between the volumes and surface areas of similar figures. The volume ratio of the larger figure to the smaller figure is ( \frac{2744}{729} = \left(\frac{a}{b}\right)^3 ), where ( a ) is the linear dimension of the larger figure and ( b ) is that of the smaller figure. Taking the cube root gives the linear scale factor ( \frac{a}{b} = \frac{14}{9} ). The surface area ratio, which is the square of the scale factor, is ( \left(\frac{14}{9}\right)^2 = \frac{196}{81} ). Given the surface area of the larger figure is 392 mm², the surface area of the smaller figure is ( 392 \times \frac{81}{196} = 162 ) mm².
What is similar thing about surface area and volume?
On a very basic level, surface area and volume are both ways to measure 3-demensional figures.
How do you find the ratio of two similar 3 dimensional figures when only given the surface area?
Notice the exponents in these two statements.Those little tiny numbers tell the whole big story:(the ratio of the surface areas of similar figures) = (the ratio of their linear dimensions)2(the ratio of the volumes of similar solids) = (the ratio of their linear dimensions)3
As a cell becomes smaller its surface-area-to-volume ratio?
The surface area to volume ratio decreases - assuming the shape remains similar.
What are the surface areas of two similar figures are 27 and 1331 if the volume of the smaller one is 18 then what is the larger ones volume?
The ratio of the surface areas of two similar figures is equal to the square of the ratio of their corresponding linear dimensions. Given the surface areas are 27 and 1331, the ratio of their corresponding linear dimensions is the square root of ( \frac{1331}{27} ). Since the volume ratio is the cube of the linear dimension ratio, we can find the larger volume by calculating ( \frac{1331}{27} ) and then multiplying the smaller volume (18) by the cube of that ratio. The larger volume is therefore ( 18 \times \left(\frac{1331}{27}\right)^{\frac{3}{2}} = 486 ).
How do you find the surface area of two similar solids?
you put: a squared over b squared = surface area of the smaller solid over surface area of the bigger solid
Do figures with the same volume always have the same surface area?
figures with the same volume does not have the same surface area.
The surface areas of two similar hexagonal prisms are 882 and1058 What is the scale factor of the smaller prism to the larger prism?
It is 21/23.
Formula for surface area of a rectangle?
actually surface area is always of 3 -d figures not for 2 d figures. area of rectangle= length x breadth.. remember never use surface area term for 2d figures. :)
Volumes of 2-D dimensional figures?
2D figures have surface area, but no volume.
What is an extrusive igneous rock with a composition similar to granite but with smaller crystals?
An extrusive igneous rock with a composition similar to granite but with smaller crystals is called rhyolite. Rhyolite forms from the rapid cooling of magma at the Earth's surface, resulting in fine-grained crystals. It is light in color and rich in silica, similar to granite.
