SOLUTION: the ratio of the volumes of two similar rectangular prisms is 125:64. What is the ratio of their base areas?
Algebra.Com
Question 935773: the ratio of the volumes of two similar rectangular prisms is 125:64. What is the ratio of their base areas?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula for the volume of a rectangular prism is area of the base * the height.
the base is equal to length * width.
the formula for the volume of a rectangular prism becomes length * width * height.
the ratio of the volume of a three sided figure is the ratio of their corresponding sides cubed.
so if the ratio of their volumes is 125/64, then the ratio of their corresponding sides id 5/4 because 5^3 = 125 and 4^3 = 64.
since the base area is equal to length * widfth, then the ratio of the areas becomes 5^2 / 4^2 which is equal to 25/16.
the ratio of the base area becomes 25/16.
to confirm, use an example:
original prism has dimensions as shown below:
length = 20
width = 40
height = 60
volume = 20 * 40 * 60 = 48000
base area = 20 * 40 = 800
prims that has sides in a ratio of 5/4 to original prism is shown below:
length = 20 * 5/4 = 25
width = 40 * 5/4 = 50
height = 60 * 5/4 = 75
volume = 25 * 50 * 75 = 93750
base area = 25 * 50 = 1250
ratio of the volumes = 93750 / 48000 = 1.953125
ratio of the base areas = 1250 / 800 = 1.5625
125/64 = 1.953125
25/16 = 1.5625
the formulas work.
the ratio of the volume is 125/64
the ratio of the base area is 25/16
RELATED QUESTIONS
The ratio of the volumes of two similar hexagonal prisms is 343:1331. What is the ratio... (answered by greenestamps)
The corresponding edges of two similar triangular prisms are in the ratio 3:5. What is... (answered by jim_thompson5910)
The ratio of the surface areas of two rectangular right prisms is 64:81. What is the... (answered by Alan3354)
the volumes of two similar cones are in the ratio 64:216.what is the ratio of their... (answered by Alan3354)
If the scale factor of two similar solids is 3:14, what is the ratio of their... (answered by Alan3354)
Two cones are similar, the ratio of their surface areas is 4 : 1
What is the ratio of... (answered by richard1234)
the ratio of the surface areas of two similar right cylinders is 25 to 4. what as the... (answered by ikleyn)
Ratio of surface areas of two cubes is 1:4. find the ratio of their... (answered by stanbon)
The volumes of two spheres are in a ratio of 8:216. What is the ratio of their... (answered by Alan3354)