If a cable is 42 ft long and is divided into lengths of a ratio of 3 to 4 what are the two lengths into which the cable is divided?
Ratio 3:4
= 3 parts of 42: 4 parts of 42 Total number of parts = 7
= (42/7)x3 : (42/7)x4
= 18ft : 24ft
Soln: the two lengths of cable are 18ft and 24ft.
6002 to 2001
The ratio of their surface areas is the square of the ratio of the lengths. Since the ratio of the lengths is 4-1, then the ratio of the surface areas is 4^2-1^2 or 16-1.
ratio of volumes is the cube of the ratio of lengths radii (lengths) in ratio 3 : 4 → volume in ratio 3³ : 4³ = 27 : 64
The ratio of their volumes is 23^3 = 12167.
The ratio is 57 cubed. This answer does not depend on the fact that you are comparing two similar pyramids; it works the same for two cubes, two spheres, etc. - in general, for any two similar 3D objects.
6002 to 2001
The ratio of areas is the square of the ratio of lengths. Ratio lengths = 1 : 2 → ratio areas = 1² : 2² = 1 : 4 → if the lengths are doubled, the areas of quadrupled (multiplied by 4).
The ratio of their surface areas is the square of the ratio of the lengths. Since the ratio of the lengths is 4-1, then the ratio of the surface areas is 4^2-1^2 or 16-1.
As volume is length x length x length, cube the ratio of the lengths, thus: Ratio of lengths = 2 : 5 ⇒ Ratio of volumes = 23 : 53 = 8 : 125
It is 5474/1850 = 2737/925 which cannot be simplified further.
If the lengths are in the ratio 3:5, then the surface areas are in the ratio 9:25.
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.
ratio of volumes is the cube of the ratio of lengths radii (lengths) in ratio 3 : 4 → volume in ratio 3³ : 4³ = 27 : 64
Area = length x length Therefore the ratio of areas of two similar objects is the square of the ratio of lengths. Lengths - 1 : 41 Areas - 12 : 412 = 1 : 1681
Their perimeters are in the same ratio.
200 divided in the ratio of 19 = 10.526315789473685
240 divided into the ratio 53 = 4.528301886792453