Question

Julia, an archaeology students, needs to dig 6 cylindrical pits at an archaeological site. Each pit will be 8 feet in diameter and 6 feet deep. Since she needs to work slowly and carefully, Julia can remove dirt at an average rate of 3 cubic feet per hour. Which of the following values is closest to the number of hours it will take Julia to dig all 6 pits?

(Note: The volume, , of a cylinder with radius and height is ; .)
200
400
100
800
600

Answer 1

it will take Julia approximately 603 hours to dig all 6 pits.

Explanation:

To find the number of hours it will take Julia to dig all 6 pits, you can first find the volume of a single pit. The volume of a cylinder is given by the formula:

Volume = πr^2h

Where r is the radius of the cylinder and h is the height of the cylinder.

The radius of each pit is half of the diameter, or 8 feet / 2 = 4 feet. The height of each pit is 6 feet.

Substituting these values into the formula, you get:

Volume = π * 4^2 * 6

= π * 16 * 6

= 96π

Since Julia can remove dirt at a rate of 3 cubic feet per hour, she can dig a single pit in 96π / 3 cubic feet per hour = 32π / 1 hour.

Since there are 6 pits, it will take her a total of 6 * (32π / 1 hour) = 192π / 1 hour to dig all of the pits.

The value 192π is approximately 603, so it will take Julia approximately 603 hours to dig all 6 pits.