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.
Okay, so I really hope that you can read all my work. I just spent the last 45 mins doing this problem as neatly as possible with as much detail as possible. So, I really hope my work doesn't confuse you.
My Final Answers were: JI= 40 units (found using the Pythagorean theorem) IM= 66.66 units = 66 and 2/3rds (found by dividing the length of JL by the cosine of ∠JIM ) LM=42.66 units = 42 and 2/3rds (found by IM= 24+LM; solve for LM since we know IM=66.66) JM= 53.33 units= 53 and (1/3rd) (found by using the Pythagorean theorem; this time using JI as "a" and IM as c)
6 Answer: The worm slithers 48 inches in an hour. The snail slithers 52 inches in an hour. If we start by making both the races into equations we get 5w+4s=448 inch and 2w+3s=252 inch. If we then add both the equations together we get 7w+7s=700 inch. Then we divide it all to get 1w+1s=100 inch. Then we can subtract the second race from the first to get 3w+1s=196 inch. We now know that 2w=96 inch, and can therefor divide whit 2 to find out w=48. We can then figure out how fast the snail is moving by multiplying 48 whit w and dividing the answer by s.
7 A 3 scoops $1.28 2 scoops $.87 1.28-.87= 41 .87-.41-.41= 06. A cone costs $.06 and one scoop ice cream costs $.41 B. .06+.41•4=$1.70
8 A. Delivery is $20. One cord is $120. B. 1 1/2 cord costs $200. ($180 for the cords and $20 for the delivery)