Applications of Perimeter, Area, and Volume: Use 3.14 for πand include the correct units. Arun's

step 1 We have two fish tanks. Model A, which is dimensions of 30 inches by 10 inches by 14 inches, and

Applications of Perimeter, Area, and Volume: Use 3.14 for...

Applications of Perimeter, Area, and Volume: Use 3.14 for $\pi$ and include the correct units. Arun's Pet Supplies sells two medium-sized rectangular fish tanks. Model A has dimensions of $30^{\prime \prime} \times 10^{\prime \prime} \times 14^{\prime \prime}$ while model $B$ has dimensions of $24^{\prime \prime} \times 13^{\prime \prime} \times 16^{\prime \prime}$ a) How many cubic inches of water will each tank hold? b) How many gallons of water will each tank hold? (Hint: Change cubic inches to cubic feet, then use the relationship $1 \mathrm{ft}^{3}=7.48 \mathrm{gal}$)

Applications of Perimeter, Area, and Volume: Use 3.14 for $\pi$ and include the correct units. Arun's Pet Supplies sells two medium-sized rectangular fish tanks. Model A has dimensions of
$30^{\prime \prime} \times 10^{\prime \prime} \times 14^{\prime \prime}$ while model $B$ has dimensions of $24^{\prime \prime} \times 13^{\prime \prime} \times 16^{\prime \prime}$
a) How many cubic inches of water will each tank hold?
b) How many gallons of water will each tank hold? (Hint: Change cubic inches to cubic feet, then use the relationship $1 \mathrm{ft}^{3}=7.48 \mathrm{gal}$)

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Volume of a Rectangular Prism

The volume of a rectangular prism is calculated by multiplying its length, width, and height. This concept is critical in determining the capacity of three-dimensional objects, such as fish tanks, and forms the basis for understanding how much space an object occupies.

Unit Conversion in Volume Measurement

Unit conversion involves translating measurements from one unit to another using conversion factors. In the context of this problem, converting cubic inches to cubic feet and then to gallons ensures that volume is expressed in meaningful, practical terms. This process is essential in many real-world applications where measurements need to be adapted to different units for analysis or communication.

Transcript

00:01 We have two fish tanks.

00:02 Model a, which is dimensions of 30 inches by 10 inches by 14 inches, and model b, which is dimensions of 24 inches by 13 by 16 inches.

00:11 So for part a, we have to find how many cubic inches each model, each fish tank can hold.

00:17 So for model a, to find the cubic inches of volume of this rectangular prism, we multiply length times width times height.

00:26 So 30 times 10, times 14.

00:30 So we get 300 times 14, which is equal to 4 ,200 inches cute.

00:40 And for the second model, we do the same thing.

00:44 Since it's the same shape, rectangular prism, but with a different dimension.

00:48 So we have 24 multiplied by 13, 13, and multiplied by 16.

00:55 So we can put these values into a calculator.

00:59 And we get that the total volume or cubic inches that this model can hold is 4 ,992 cubic inches.

01:10 And for part a, for part b, this question is asking how many gallons can each one hold? we're given the information that about one cubic feet is equal to 7 .48 gallons.

01:25 So one cubic feet equal to about 7 .48 gallons.

01:33 Balance .48 gallons.

01:43 And the first thing we need to do is realize that these values are in inches.

01:47 So we need to convert these into feet...

Please give Ace some feedback