Question

PLEASE HELP WITH DETAILED ANSWER ASAP FOR 50 POINTS!! You notice these two old suitcases stacked in the closet. The smaller suitcase is 25 in x 8 in x 9 in, and the larger suitcase is 75 in x 20 in x 18 in.

1. The big suitcase is how many times larger than the smaller suitcase?

2. You decide to use the larger suitcase to transport rectangular prism watermelons back home. Though their dimensions vary, the average rectangular watermelon has a volume of roughly 720 cubic inches. If one of these watermelons is about 10 inches long and 9 inches wide, about how tall would it be?

3. If the average rectangular watermelon has a volume of 720 cubic inches, what’s the maximum number of watermelons you’ll be able to bring home in your larger suitcase, assuming all you have in the suitcase are watermelons?

Answer 1

Explanation:

1. To find out how many times larger the big suitcase is than the small suitcase, we need to compare their volumes. The volume of the small suitcase is:

25 in x 8 in x 9 in = 1800 cubic inches

The volume of the large suitcase is:

75 in x 20 in x 18 in = 27,000 cubic inches

To find out how many times larger the big suitcase is, we can divide its volume by the volume of the small suitcase:

27,000 cubic inches ÷ 1800 cubic inches = 15

Therefore, the big suitcase is 15 times larger than the small suitcase.

2. To find the height of the watermelon, we need to use the formula for volume of a rectangular prism:

V = l x w x h

We know that the volume is 720 cubic inches, the length is 10 inches, and the width is 9 inches. Rearranging the formula to solve for the height, we get:

h = V ÷ (l x w)

h = 720 cubic inches ÷ (10 inches x 9 inches)

h ≈ 8 inches

Therefore, the watermelon would be about 8 inches tall.

3. To find out how many watermelons you can fit in the large suitcase, we need to divide its volume by the volume of one watermelon:

27,000 cubic inches ÷ 720 cubic inches = 37.5

However, we can't fit a decimal number of watermelons in the suitcase, so we need to round down. Therefore, the maximum number of watermelons you can bring home in the larger suitcase is 37.