QuestionFind the volume of Lin's aquarium with dimensions $\frac{7}{2} \mathrm{ft}$ (length), $\frac{4}{3} \mathrm{ft}$ (width), and $\frac{3}{2} \mathrm{ft}$ (height).

Studdy Solution

STEP 1

Assumptions1. The length of the aquarium is $\frac{7}{} \mathrm{ft}$ . The width of the aquarium is $\frac{4}{3} \mathrm{ft}$
3. The height of the aquarium is $\frac{3}{} \mathrm{ft}$
4. The volume of a rectangular prism (which is the shape of the aquarium) is calculated by multiplying the length, width, and height.

STEP 2

We need to find the volume of the aquarium. We can do this by multiplying the length, width, and height.
$Volume = Length \times Width \times Height$

STEP 3

Now, plug in the given values for the length, width, and height to calculate the volume.
$Volume = \frac{7}{2} \mathrm{ft} \times \frac{}{3} \mathrm{ft} \times \frac{3}{2} \mathrm{ft}$

STEP 4

First, multiply the fractions $\frac{7}{2}$ and $\frac{4}{3}$ .
$\frac{7}{2} \times \frac{4}{3} = \frac{7 \times4}{2 \times3} = \frac{28}{6}$

STEP 5

implify the fraction $\frac{28}{}$ to get the intermediate volume.
$\frac{28}{} = \frac{14}{3} \mathrm{ft}^2$

STEP 6

Now, multiply the intermediate volume $\frac{14}{3} \mathrm{ft}^2$ with the height $\frac{3}{2} \mathrm{ft}$ to get the volume of the aquarium.
$Volume = \frac{14}{3} \mathrm{ft}^2 \times \frac{3}{2} \mathrm{ft}$

STEP 7

Multiply the fractions $\frac{14}{3}$ and $\frac{3}{2}$ .
$\frac{14}{3} \times \frac{3}{2} = \frac{14 \times3}{3 \times2} = \frac{42}{6} \mathrm{ft}^3$

STEP 8

implify the fraction $\frac{42}{6}$ to get the volume of the aquarium.
$Volume = \frac{42}{6} =7 \mathrm{ft}^3$ The volume of Lin's second aquarium is $7 \mathrm{ft}^3$ .

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QuestionFind the volume of Lin's aquarium with dimensions $\frac{7}{2} \mathrm{ft}$ (length), $\frac{4}{3} \mathrm{ft}$ (width), and $\frac{3}{2} \mathrm{ft}$ (height).

Studdy Solution

STEP 1

STEP 2

We need to find the volume of the aquarium. We can do this by multiplying the length, width, and height.
$Volume = Length \times Width \times Height$

STEP 3

Now, plug in the given values for the length, width, and height to calculate the volume.
$Volume = \frac{7}{2} \mathrm{ft} \times \frac{}{3} \mathrm{ft} \times \frac{3}{2} \mathrm{ft}$

STEP 4

First, multiply the fractions $\frac{7}{2}$ and $\frac{4}{3}$ .
$\frac{7}{2} \times \frac{4}{3} = \frac{7 \times4}{2 \times3} = \frac{28}{6}$

STEP 5

implify the fraction $\frac{28}{}$ to get the intermediate volume.
$\frac{28}{} = \frac{14}{3} \mathrm{ft}^2$

STEP 6

Now, multiply the intermediate volume $\frac{14}{3} \mathrm{ft}^2$ with the height $\frac{3}{2} \mathrm{ft}$ to get the volume of the aquarium.
$Volume = \frac{14}{3} \mathrm{ft}^2 \times \frac{3}{2} \mathrm{ft}$

STEP 7

Multiply the fractions $\frac{14}{3}$ and $\frac{3}{2}$ .
$\frac{14}{3} \times \frac{3}{2} = \frac{14 \times3}{3 \times2} = \frac{42}{6} \mathrm{ft}^3$

STEP 8

implify the fraction $\frac{42}{6}$ to get the volume of the aquarium.
$Volume = \frac{42}{6} =7 \mathrm{ft}^3$ The volume of Lin's second aquarium is $7 \mathrm{ft}^3$ .

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QuestionFind the volume of Lin's aquarium with dimensions 72ft\frac{7}{2} \mathrm{ft}27​ft (length), 43ft\frac{4}{3} \mathrm{ft}34​ft (width), and 32ft\frac{3}{2} \mathrm{ft}23​ft (height).

Studdy Solution

STEP 1

STEP 2

We need to find the volume of the aquarium. We can do this by multiplying the length, width, and height.Volume=Length×Width×HeightVolume = Length \times Width \times HeightVolume=Length×Width×Height

STEP 3

Now, plug in the given values for the length, width, and height to calculate the volume.Volume=72ft×3ft×32ftVolume = \frac{7}{2} \mathrm{ft} \times \frac{}{3} \mathrm{ft} \times \frac{3}{2} \mathrm{ft}Volume=27​ft×3​ft×23​ft

STEP 4

First, multiply the fractions 72\frac{7}{2}27​ and 43\frac{4}{3}34​.72×43=7×42×3=286\frac{7}{2} \times \frac{4}{3} = \frac{7 \times4}{2 \times3} = \frac{28}{6}27​×34​=2×37×4​=628​

STEP 5

implify the fraction 28\frac{28}{}28​ to get the intermediate volume.28=143ft2\frac{28}{} = \frac{14}{3} \mathrm{ft}^228​=314​ft2

STEP 6

Now, multiply the intermediate volume 143ft2\frac{14}{3} \mathrm{ft}^2314​ft2 with the height 32ft\frac{3}{2} \mathrm{ft}23​ft to get the volume of the aquarium.Volume=143ft2×32ftVolume = \frac{14}{3} \mathrm{ft}^2 \times \frac{3}{2} \mathrm{ft}Volume=314​ft2×23​ft

STEP 7

Multiply the fractions 143\frac{14}{3}314​ and 32\frac{3}{2}23​.143×32=14×33×2=426ft3\frac{14}{3} \times \frac{3}{2} = \frac{14 \times3}{3 \times2} = \frac{42}{6} \mathrm{ft}^3314​×23​=3×214×3​=642​ft3

STEP 8

implify the fraction 426\frac{42}{6}642​ to get the volume of the aquarium.Volume=426=7ft3Volume = \frac{42}{6} =7 \mathrm{ft}^3Volume=642​=7ft3The volume of Lin's second aquarium is 7ft37 \mathrm{ft}^37ft3.

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QuestionFind the volume of Lin's aquarium with dimensions $\frac{7}{2} \mathrm{ft}$ (length), $\frac{4}{3} \mathrm{ft}$ (width), and $\frac{3}{2} \mathrm{ft}$ (height).

We need to find the volume of the aquarium. We can do this by multiplying the length, width, and height.
$Volume = Length \times Width \times Height$

Now, plug in the given values for the length, width, and height to calculate the volume.
$Volume = \frac{7}{2} \mathrm{ft} \times \frac{}{3} \mathrm{ft} \times \frac{3}{2} \mathrm{ft}$

First, multiply the fractions $\frac{7}{2}$ and $\frac{4}{3}$ .
$\frac{7}{2} \times \frac{4}{3} = \frac{7 \times4}{2 \times3} = \frac{28}{6}$

implify the fraction $\frac{28}{}$ to get the intermediate volume.
$\frac{28}{} = \frac{14}{3} \mathrm{ft}^2$

Now, multiply the intermediate volume $\frac{14}{3} \mathrm{ft}^2$ with the height $\frac{3}{2} \mathrm{ft}$ to get the volume of the aquarium.
$Volume = \frac{14}{3} \mathrm{ft}^2 \times \frac{3}{2} \mathrm{ft}$

Multiply the fractions $\frac{14}{3}$ and $\frac{3}{2}$ .
$\frac{14}{3} \times \frac{3}{2} = \frac{14 \times3}{3 \times2} = \frac{42}{6} \mathrm{ft}^3$

implify the fraction $\frac{42}{6}$ to get the volume of the aquarium.
$Volume = \frac{42}{6} =7 \mathrm{ft}^3$ The volume of Lin's second aquarium is $7 \mathrm{ft}^3$ .