1. The dimensions of the tank should be 20 by 20 by 20. The hint is telling you that a tank that is 2 by 2 by 2 has a volume of 8, so, if you increase the size of the dimensions, you can reach 8,000 with the same digit of 2. Don't forget that the formula for the volume of a rectangular prism is lwh.
2. Since our aquarium is a square tank that is 20 by 20 by 20, each side on the top is 20 inches long. We have 4 sides, so the perimeter is 4 x 20, or 80. The perimeter of the top of our tank is 80 in². As for the base, we already know that each side is 20, so, in order to find the area of the base, we just multiply 20 x 20 to get 400. The area of the base of the tank is 400 in².
3. Another rectangular prism with a volume of 8,000 might have dimensions of 40 by 20 by 10. These, multiplied together, equal 8,000, using the formula for the volume of a rectangular prism.
To find the dimensions of the rectangular prism that equal 8,000, I mostly just use trial and error. It helps if you think about it as 8, as shown in the first problem, or if you list the factors of 8. For instance, for number 3, I just used the factors of 8 to find some possible dimensions.
8 - 1, 2, 4, 8 For number 3, I used the factors 1, 2, and 4. To change it from 8 to 8,000, I just changed 1 to 10, 2 to 20, and 4 to 40.
----------------------------------------------- Define x : ----------------------------------------------- Let the width be x Width = x Length = 4x + 7
----------------------------------------------- Formula : ----------------------------------------------- Perimeter = 2 (Length + Width)
Perimeter = 74 2(4x + 7 + x) = 74 // sub length and width into the equation 2(5x + 7) = 74 // combine like terms 10x + 14 = 74 // Apply distributive property 10x = 60 // Take away 14 from both sides x = 6 // Divide by 10 on both sides
---------------------------------------------------------------------------------------------- Answer: The length is 31mm and its width 6mm. ----------------------------------------------------------------------------------------------
All you need to do is insert the numbers they gave you into the L and H spots. So:
s= 0.78(1.25)^1.67 ___________ 0.93^1.17 Solve the top by putting the equation into a calculator and then the same for the bottom. After that divide the top's solution with the bottom and you should have found the answer
