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Nadya [2.5K]
3 years ago
12

Two similar solids have a scale factor of 3:4. What is the ratio of their volumes, expressed in lowest terms?

Mathematics
2 answers:
dalvyx [7]3 years ago
8 0
The ratio of the volumes will be equal to the ratio of the cubes of the sides. Thus:
Volume ratio:
3³: 4³
27 : 64
vlabodo [156]3 years ago
6 0

Answer:

The ratio of their volumes is equal to \frac{27}{64}

Step-by-step explanation:

we know that

If two figures are similar, then the ratio of its volumes is equal to the scale factor elevated to the cube

Let

z-----> the scale factor

x------> the volume of the dilated figure

y-------> the volume of the original figure

so

z^{3}=\frac{x}{y}

we have

z=\frac{3}{4}

substitute

(\frac{3}{4})^{3}=\frac{x}{y}

(\frac{27}{64})=\frac{x}{y}

therefore

The ratio of their volumes is equal to \frac{27}{64}

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The smaller rectangle at the top:

The equation to find the area of a rectangle is
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a = l · w
Put in the values
a = 18 · 3
a = 54

Since the smaller rectangle at the bottom has the same length and width, it has the same area. 

The bigger rectangle in the middle:

a = l · w
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Now add all of the areas together to get the answer!

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Răspuns:

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