Question

[Been stuck on this one for a while, please help if you can]


In order for you to carry a bag on the plane, it must fit inside the carry-on Baggage Check Box.

The carry-on Baggage Check Box has dimensions of approximately 22 inches x 14 inches x 9 inches.

Your black bag has a height of 18 inches, a depth of 12 inches and a width of 8 inches.

Your blue bag has a height of 18 inches, a depth of 15 inches and a width of 10 inches.


What is the volume of the Carry-on Baggage Check Box?

What is the volume of the black bag?

What is the volume of the blue bag?

Which bag will definitely fit in the Check Box? Explain.


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You notice these two old suitcases stacked in the closet. The smaller suitcase is 25 inches x 8 inches x 9 inches and the larger suitcase is 75 inches x 20 inches x 18 inches.



The bigger suitcase is how many times larger than the smaller suitcase? HINT: You will need to divide on this one.





You decide to use the larger suitcase to transport rectangular prism watermelons back home. The watermelons are about 720 cubic inches. If one of the watermelons is about 10 inches long and 9 inches wide, about how tall would it be? (Hint: V=LxWxH, so plug h in 720=10x9xH and solve for H).







If the watermelons are about 720 cubic inches, what is the MAXIMUM amount of watermelons you’ll be able to bring home in your larger suitcase, assuming all you have in the suitcase is the watermelons. (Hint: Divide the larger suitcase volume and the volume of the watermelon).

Answer 1

The given dimensions of the, Check Box, bag, suitcase, and watermelons, we have;

First part;

Volume of the Check box is 2,772 in.³

Volume of the black bag is 1728 in.³

Volume of the blue bag is 2700 in.³

• The bag that will definitely fit in the Check Box is; The black bag

Second part;

• The number of times, the bigger suit case is larger than the smaller suit case is 15 times

Third part;

• The height of the watermelon = 8 inches

• The maximum number of watermelon the larger suitcase can carry is 36 watermelon

How can the volume of the suitcases be found?

Volume of the Carry-on baggage Check box, V_c can be found as follows;

V_c = 22 × 14 × 9 = 2772

• Volume of the Check box, V_c = 2,772 in.³

Volume of the black bag, V_b, can be found as follows;

V_b = 18 × 12 × 8 = 1728

• Volume of the black bag, V_b = 1728 in.³

Volume of the blue bag, V_bl, can be found as follows;

V_bl = 18 × 15 × 10 = 2700

• Volume of the blue bag, V_bl = 2700 in.³

Given that the height, depth and width of the black bag are smaller than the height, depth and width of the check box

• The bag that will definitely fit in the Check Box is; The black bag

Second part;

Volume of the smaller suitcase is found as follows;

V_s = 25×8×9 = 1800

Volume of the bigger suitcase is found as follows;

V_b = 75 × 20 × 18 = 27,000

The number of times, the bigger suitcase is larger than the smaller suitcase is therefore;

n = 27,000 ÷ 1809 = 15

• The number of times, the bigger suit case is larger than the smaller suit case is 15 times

Third part

The volume of the watermelon = 720 in.³

Which gives;

10 × 9 × H = 720

H = 720 ÷ (10 × 9) = 8

• The height of the watermelon = 8 inches

To maximize the number of watermelons, we have;

The length, 10, is a factor of 20

The width, 9, is a factor of 18

Therefore, we have;

Two rows of watermelon, and two layers of watermelon

Number of watermelon in a row is therefore;

R = 75 ÷ 8 ≈ 9

Maximum number of watermelon is therefore;

Max_n = 9 × 2 × 2 = 36

• The maximum number of watermelon the larger suitcase can carry is 36 watermelon

Learn more about finding the volume of a figure here:

https://brainly.com/question/1452651