125/8 or (5/2)3
If the ratio of the dimensions of the larger prism to the smaller prism is r then the ratio of their volumes is r^3.
If the sides of two shapes are in the ratio of A : B, then their volumes are in the ratio A3 : B3, thus: ratio of volumes = 125 : 9 ratio of sides = 3√125 : 3√9 ~= 5: 2.08 (~= 2.4 : 1) Have you got the volumes correct? I suspect the second should be 8cm3 not 9cm3, because then the volumes would be 125cm3 and 8cm3 and: ration of volumes = 125 : 8 ratio of sides = 3√125 : 3√8 = 5 : 2 (= 2.5 : 1)
You cannot because the volumes of the cones also depend on their heights.
The ratio of their heights is 9:4
Where objects are SIMILAR (scale versions of each other) then the ratio of linear measurements is a : b, the ratio of areas is a2 : b2 and the ratio of volumes is a3 : b3. As the area ratio is 4 : 25 = a2 : b2 = 22 : 52 then the ratio of their heights is a : b = 2 : 5.
It is 27 : 343.
If the ratio of the dimensions of the larger prism to the smaller prism is r then the ratio of their volumes is r^3.
If the sides of two shapes are in the ratio of A : B, then their volumes are in the ratio A3 : B3, thus: ratio of volumes = 125 : 9 ratio of sides = 3√125 : 3√9 ~= 5: 2.08 (~= 2.4 : 1) Have you got the volumes correct? I suspect the second should be 8cm3 not 9cm3, because then the volumes would be 125cm3 and 8cm3 and: ration of volumes = 125 : 8 ratio of sides = 3√125 : 3√8 = 5 : 2 (= 2.5 : 1)
You cannot because the volumes of the cones also depend on their heights.
As the two prisms are similar there are ratios between them. The ratio of the lengths is 4 : 12 = 1 : 3 The ratio of volumes is the cubs of the ratio of lengths. → The volumes are in the ratio of 1³ : 3² = 1 : 27 As the a smaller prism has a volume of 24 cm³, the larger prism has a volume 27 times larger → volume larger prism = 27 × 24 cm³ = 648 cm³
If the ratio is 2 : 7 then the volumes are in the ratio 8 : 343.
The answer depends on whether or not the shapes are similar. If they are, then the ratio of volumes is the cube of the ratio of the linear dimensions.
The ratio of their volumes is 23^3 = 12167.
The ratio of their heights is 9:4
Where objects are SIMILAR (scale versions of each other) then the ratio of linear measurements is a : b, the ratio of areas is a2 : b2 and the ratio of volumes is a3 : b3. As the area ratio is 4 : 25 = a2 : b2 = 22 : 52 then the ratio of their heights is a : b = 2 : 5.
The ratio of volumes is directly proportional to the cube of the ratio of their sides. And, incidentally, all cubes are similar.
If the ratio of side lengths is 49 (that is 49 to 1) then the ratio of their volumes is 493 to 1, which is 117,649 to 1.