A landscaper dug holes. It takes him 1 hour to dig a hole 2 feet deep, 2 feet long and 2 feet wide. Assuming everything remains the same, how many hours would it take him to dig a hole 4 feet deep, 4 feet long and 4 feet wide?
the volume of the first hole is 2x2x2 or 8 cubic feet
so his rate is 9 cubic feet/hour
the second hole is 4x4x4 or 64 cubic feet.
so if he can dig 8 cubic feet in 1 hour, how many hours do you think it would take him to dig 64 cubic feet?
I am confused.
You said in your first statement that his rate is 9 cubic feet/hour. But you also state that he can dig 8 cubic feet in 1 hour.
I am assuming that if he can dig 8 cubic feet in 1 hour that it would take him 8 hours to dig 64 cubic feet. (64 cu. ft divided by 8 cu. ft.) Correct?
clearly a typo,
yes, you are right, it would take 8 hours.
Thank you Dr. Reiny.
50 feet long and 30 feet wide with 9 feet tall, what is the volume of the interior of the second floor
To find out how many hours it would take the landscaper to dig a larger hole, we need to compare the volumes of the two holes. The volume of a rectangular prism (our hole) is found by multiplying the length, width, and height.
Let's start by finding the volume of the first hole:
Volume = length * width * height
Volume = 2 feet * 2 feet * 2 feet
Volume = 8 cubic feet
Now, let's find the volume of the larger hole:
Volume = length * width * height
Volume = 4 feet * 4 feet * 4 feet
Volume = 64 cubic feet
Since the larger hole is 8 times bigger than the first hole (64 cubic feet / 8 cubic feet), it will take the landscaper 8 times longer to dig it.
So, if it took him 1 hour to dig the first hole, it will take him 8 hours to dig the larger hole.