Question

Scientists are drilling a hole in the ocean floor to learn more about the​ Earth's history. ​ Currently, the hole is in the shape of a cylinder whose volume is approximately 3500 cubic feet and whose height is 4.3 miles. Find the radius of the hole to the nearest hundredth of a foot. ​ (Hint: Make sure the same units of measurement are​ used.)

Answer 1

The radius of the cylindrical hole with a volume of approximately 3500 cubic feet and height of 4.3 miles is approximately 0.22 feet to the nearest hundredth of a foot.

Step-by-step explanation:

To find the radius of the hole that scientists are drilling in the ocean floor to learn more about the Earth's history, we will use the formula for the volume of a cylinder, which is V = πr²h, where V is the volume, r is the radius, and h is the height. Given that the volume is approximately 3500 cubic feet and the height is 4.3 miles, we need to convert the height to feet since the volume is given in cubic feet. There are 5280 feet in a mile, so the height in feet is 4.3 miles × 5280 feet/mile = 22704 feet.

Now, we plug the values into the volume formula and solve for r:
πr²(22704 feet) = 3500 cubic feet
r² = 3500 cubic feet / (π × 22704 feet)
r² = 3500 / (3.14159 × 22704)
r² ≈ 0.04907
r ≈ √0.04907
r ≈ 0.2215 feet

Therefore, the radius of the hole to the nearest hundredth of a foot is approximately 0.22 feet.

Answer 2

0.22 feet

Step-by-step explanation:

Volume of cylinder = 3500 cubic feet = v

Height of cylinder = 4.3 miles

Convert to miles to feet

1 mile = 5280 feet

4.3 miles = 4.3×5280 = 22704 feet = h

Volume of cylinder

`v=\pi r^2h\\\Rightarrow r=\sqrt{(v)/(\pi h)}\\\Rightarrow r=\sqrt{(3500)/(\pi 22704)}\\\Rightarrow r=0.22\ ft`

The radius of the hole is 0.22 feet (ignoring the thickness of the cylinder).