I need help with just two questions. Can you help me with them please? Thank you so much!
1. School Materials, Inc., packs 1-centimeter cubes in boxes that are 10 centimeters long, 12-centimeters wide, and 8 centimeters high. A carton holds 2 dozen boxes of cubes with no space around the boxes. How many 1- centimeter cubes are in 1 carton?
2. In 4 hours, Clark can mow a field that is 200 meters long and 200 meters wide. If he works at the same rate, how long will it take Clark to mow a field that is 50 meters and 50 meters wide?
1)
10 * 12 * 8 * 24 = ?
2)
A = 200 * 200
A = 40,000 square meters
40,000 / 4 = 10,000 m/h
A = 50 * 50
A = 2,500 square meters
Take it from there.
Thanks!
You're welcome.
6+2=8
Of course, I'd be happy to help you with your questions! Let's tackle them one by one:
1. To find the number of 1-centimeter cubes in 1 carton, we need to determine the volume of the carton and then calculate how many cubes can fit inside that volume.
First, let's find the volume of the carton:
Volume = length × width × height
Volume = 10 cm × 12 cm × 8 cm
Volume = 960 cm³
Next, we need to calculate the volume occupied by one box of cubes:
Volume of one box = Volume of a cube
Volume of one box = (1 cm × 1 cm × 1 cm)
Volume of one box = 1 cm³
Since one box of cubes has a volume of 1 cm³, the number of cubes that can fit in the carton is equal to the volume of the carton divided by the volume of one box:
Number of cubes per carton = Volume of carton / Volume of one box
Number of cubes per carton = 960 cm³ / 1 cm³
Number of cubes per carton = 960 cubes
However, the given information states that one carton holds 2 dozen (24) boxes, so to find the total number of cubes in 1 carton, we need to multiply 960 cubes by 24:
Total number of cubes in 1 carton = 960 cubes/box * 24 boxes
Total number of cubes in 1 carton = 23,040 cubes
Therefore, there are 23,040 1-centimeter cubes in 1 carton.
2. Clark can mow a field that is 200 meters long and 200 meters wide in 4 hours. Therefore, we need to find the area of the field he can mow in 1 hour and use that to calculate the time it takes him to mow a smaller field.
To find the area of the larger field, we use the formula:
Area = length × width
Area = 200 m × 200 m
Area = 40,000 m²
Since Clark can mow a 40,000 m² field in 4 hours, we can calculate his mowing rate per hour:
Mowing rate = Area / Time
Mowing rate = 40,000 m² / 4 hours
Mowing rate = 10,000 m²/hour
Now, let's calculate the area of the smaller field:
Area = 50 m × 50 m
Area = 2,500 m²
To find the time it takes for Clark to mow the smaller field, we use the formula:
Time = Area / Mowing rate
Time = 2,500 m² / 10,000 m²/hour
Time = 0.25 hours
Therefore, it will take Clark 0.25 hours, which is equivalent to 15 minutes, to mow a field that is 50 meters long and 50 meters wide.
I hope this helps! If you have any more questions or need further clarification, please let me know.