Asked by Charles
Two pyramids are similar.
The surface area of the first is 250 and the surface area of the second is 22.5.
The heights of the pyramids are in a ratio of _ : _
The volumes of the pyramids are in a ratio of _ : _
Two pyramids are similar.
The surface area of the first is 250 and the surface area of the second is 22.5.
The heights of the pyramids are in a ratio of _ : _
The volumes of the pyramids are in a ratio of _ : _
Two pyramids are similar.
Answers
Answered by
oobleck
area:area = (height:height)^2
volume:volume = (height:height)^3
volume:volume = (height:height)^3
Answered by
Bosnian
If the scale factor (ratio between linear
measurements of two similar figures) is k then:
The ratio between area of those two similar figures will be k²
The ratio between volume of those two similar figures will be k³
The ratio between area = 250 / 22.5 = k²
k = √ ( 250 / 22.5 ) = √ ( 2.5 ∙ 100 / 2.5 ∙ 9 ) =
√ ( 100 / 9 ) = √ 100 / √ 9 = 10 / 3
The heights of the pyramids is linear measurements.
The heights of the pyramids are in a ratio of k = 10 : 3
The volumes of the pyramids are in a ratio of k³ = 10³ : 3³ = 1000 : 27
measurements of two similar figures) is k then:
The ratio between area of those two similar figures will be k²
The ratio between volume of those two similar figures will be k³
The ratio between area = 250 / 22.5 = k²
k = √ ( 250 / 22.5 ) = √ ( 2.5 ∙ 100 / 2.5 ∙ 9 ) =
√ ( 100 / 9 ) = √ 100 / √ 9 = 10 / 3
The heights of the pyramids is linear measurements.
The heights of the pyramids are in a ratio of k = 10 : 3
The volumes of the pyramids are in a ratio of k³ = 10³ : 3³ = 1000 : 27
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