Question

a cylinder is full at 471 cubic centimeters and has a radius of 5 centimeters. it currently contains 314 cubic centimeters of water. what is the difference between the height of the water in the full cylinder and the height when 314 cubic centimeters of water remains in the cylinder? use 3.14 for pi. enter your answer in the box.

Explanation:

Step1: Recall the volume formula for a cylinder

The volume \( V \) of a cylinder is given by \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height. We can solve for \( h \) as \( h=\frac{V}{\pi r^2} \).

Step2: Calculate the base area of the cylinder

Given \( r = 5 \) cm and \( \pi=3.14 \), the base area \( A=\pi r^2=3.14\times5^2 = 3.14\times25=78.5 \) square centimeters.

Step3: Find the height of the full cylinder

The volume of the full cylinder \( V_{full}=471 \) cubic centimeters. Using \( h=\frac{V}{A} \), the height \( h_{full}=\frac{471}{78.5}=6 \) centimeters.

Step4: Find the height of the cylinder with 314 cubic centimeters of water

The volume \( V_{water}=314 \) cubic centimeters. Using \( h=\frac{V}{A} \), the height \( h_{water}=\frac{314}{78.5} = 4 \) centimeters.

Step5: Calculate the difference in heights

The difference \( \Delta h=h_{full}-h_{water}=6 - 4=2 \) centimeters.

Answer:

2