Question

the interior dimensions of a restaurant refrigerator are 8 feet high, 6 feet wide, and 3 feet deep. how many cubic feet of space are in the refrigerator? to solve, use the formula for the volume of a rectangular prism. v = ℓwh v = 8•6•3 ←— substitute the known values. v = 144 ←— simplify. there are 144 cubic feet of space inside the refrigerator. remember: volume is measured in cubic units (units³). area is measured in square units (units²). perimeter is measured in units. use the volume formula for a rectangular prism, v = ℓwh, to solve. 1. find v when ℓ = 4, w = 6, and h = 2. v = 4•6•2 v = 48 units³ 2. find v when ℓ = 50, w = 30, and h = 15. 3. find h when v = 54, ℓ = 6, and w = 3. 4. find h when v = 512, ℓ = 8, and w = 8. 5. find w when v = 360, ℓ = 9, and h = 5. 6. find w when v = 48, ℓ = 2, and h = 6. 7. find ℓ when v = 108, w = 6, and h = 2. 8. find ℓ when v = 1000, h = 10, and w = 10. use the area formula for a rectangle, a = ℓw, to solve. 9. find a when ℓ = 24 and w = 3. a = 24•3 a = 72 units² 10. find a when ℓ = 9 and w = 11. 11. find w when a = 225 and ℓ = 25. 12. find w when a = 64 and ℓ = 8. 13. find ℓ when w = 4 and a = 104. 14. find ℓ when w = 13 and a = 65. sourcebook lesson 2 - 9, pages 46 - 47.

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular prism is $V = \ell wh$.

Step2: Solve problem 2

Substitute $\ell = 50$, $w = 30$, and $h = 15$ into the formula: $V=50\times30\times15 = 22500$ units³.

Step3: Solve problem 3

Given $V = 54$, $\ell = 6$, and $w = 3$. Rearrange the formula $V=\ell wh$ to $h=\frac{V}{\ell w}$. Then $h=\frac{54}{6\times3}= 3$ units.

Step4: Solve problem 4

Given $V = 512$, $\ell = 8$, and $w = 8$. Using $h=\frac{V}{\ell w}$, we have $h=\frac{512}{8\times8}=8$ units.

Step5: Solve problem 5

Given $V = 360$, $\ell = 9$, and $h = 5$. Rearrange the formula to $w=\frac{V}{\ell h}$. So $w=\frac{360}{9\times5}=8$ units.

Step6: Solve problem 6

Given $V = 48$, $\ell = 2$, and $h = 6$. Using $w=\frac{V}{\ell h}$, we get $w=\frac{48}{2\times6}=4$ units.

Step7: Solve problem 7

Given $V = 108$, $w = 6$, and $h = 2$. Rearrange to $\ell=\frac{V}{wh}$. Then $\ell=\frac{108}{6\times2}=9$ units.

Step8: Solve problem 8

Given $V = 1000$, $h = 10$, and $w = 10$. Using $\ell=\frac{V}{wh}$, we have $\ell=\frac{1000}{10\times10}=10$ units.

Step9: Recall area formula

The area formula for a rectangle is $A=\ell w$.

Step10: Solve problem 10

Substitute $\ell = 9$ and $w = 11$ into the formula: $A = 9\times11=99$ units².

Step11: Solve problem 11

Given $A = 225$ and $\ell = 25$. Rearrange to $w=\frac{A}{\ell}$. So $w=\frac{225}{25}=9$ units.

Step12: Solve problem 12

Given $A = 64$ and $\ell = 8$. Using $w=\frac{A}{\ell}$, we get $w=\frac{64}{8}=8$ units.

Step13: Solve problem 13

Given $w = 4$ and $A = 104$. Rearrange to $\ell=\frac{A}{w}$. Then $\ell=\frac{104}{4}=26$ units.

Step14: Solve problem 14

Given $w = 13$ and $A = 65$. Using $\ell=\frac{A}{w}$, we have $\ell=\frac{65}{13}=5$ units.

Answer:

1. $V = 48$ units³
2. $V = 22500$ units³
3. $h = 3$ units
4. $h = 8$ units
5. $w = 8$ units
6. $w = 4$ units
7. $\ell = 9$ units
8. $\ell = 10$ units
9. $A = 72$ units²
10. $A = 99$ units²
11. $w = 9$ units
12. $w = 8$ units
13. $\ell = 26$ units
14. $\ell = 5$ units