Question
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
oobleck
area:area = (height:height)^2
volume:volume = (height:height)^3
volume:volume = (height:height)^3
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