Question

1. the town of riverview provides a rectangular recycling bin for newspapers to each household. if the volume is 1,800 cubic inches, what is the height of the recycling bin?7. find the length of a rectangular prism with a width of 4 feet, a height of 6 feet, and a volume of 84 cubic feet.8. find the height of a rectangular prism with a width of 6 millimeters, a length of 20.5 millimeters, and a volume of 984 cubic millimeters.9. find the missing dimension of the following prism. $v=39.48m^{3}$10. find the missing dimension of the following prism. $v=56\frac{1}{4}ft^{3}$

Explanation:

Step1: Recall prism volume formula

The volume of a rectangular prism is $V = l \times w \times h$, where $l$ = length, $w$ = width, $h$ = height. We rearrange to solve for the missing dimension: $\text{Missing Dimension} = \frac{V}{l \times w}$ (or appropriate product of known dimensions).

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Problem 6:

Step1: Identify known values

$V=1840\text{ in}^3$, $l=20\text{ in}$, $w=8\text{ in}$

Step2: Solve for height $h$

$h = \frac{V}{l \times w} = \frac{1840}{20 \times 8} = \frac{1840}{160}$

Step3: Calculate final value

$h=11.5$

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Problem 7:

Step1: Identify known values

$V=84\text{ ft}^3$, $w=4\text{ ft}$, $h=6\text{ ft}$

Step2: Solve for length $l$

$l = \frac{V}{w \times h} = \frac{84}{4 \times 6} = \frac{84}{24}$

Step3: Calculate final value

$l=3.5$

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Problem 8:

Step1: Identify known values

$V=984\text{ mm}^3$, $w=6\text{ mm}$, $l=20.5\text{ mm}$

Step2: Solve for height $h$

$h = \frac{V}{l \times w} = \frac{984}{20.5 \times 6} = \frac{984}{123}$

Step3: Calculate final value

$h=8$

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Problem 9:

Step1: Identify known values

$V=39.48\text{ m}^3$, $w=1\text{ m}$, $h=8.4\text{ m}$

Step2: Solve for length $l$

$l = \frac{V}{w \times h} = \frac{39.48}{1 \times 8.4}$

Step3: Calculate final value

$l=4.7$

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Problem 10:

Step1: Convert mixed numbers to decimals

$7\frac{1}{2}=7.5\text{ ft}$, $3\frac{3}{4}=3.75\text{ ft}$, $56\frac{1}{4}=56.25\text{ ft}^3$

Step2: Solve for height $h$

$h = \frac{V}{l \times w} = \frac{56.25}{7.5 \times 3.75} = \frac{56.25}{28.125}$

Step3: Calculate final value

$h=2$

Answer:

1. $\boldsymbol{11.5}$ inches
2. $\boldsymbol{3.5}$ feet
3. $\boldsymbol{8}$ millimeters
4. $\boldsymbol{4.7}$ meters
5. $\boldsymbol{2}$ feet