A paperweight containing liquid is made up of a cone and a cylinder. The radius of the cone is 3cm with height of 4cm. The diameter is 20cm and height is 8cm.

1. Calculate the total volume of the cone and cylinder when it si empty, leaving your answer in terms of pi.
2. If the liquid fills half the cylinder when placed on a flat table find the height of the liquid in the cylinder when the paper weihgt is turned upside down.

I was expecting the radius of the cone to be the same as the radius of the cylinder.

So the cone is partially covering the circle of the cone ?

Please clarify.

Sorry, the diameter of 20cm and height of 8cm is for the cylinder.

To calculate the total volume of the cone and cylinder when it is empty, we need to find the volume of each shape separately and then add them together.

1. Volume of the cone:
The formula for the volume of a cone is V = (1/3) * π * r^2 * h.
Given:
radius (r) = 3 cm
height (h) = 4 cm
Using the values in the formula, we can calculate the volume of the cone: V_cone = (1/3) * π * (3 cm)^2 * 4 cm.

2. Volume of the cylinder:
The formula for the volume of a cylinder is V = π * r^2 * h.
Given:
diameter (d) = 20 cm
radius (r) = 0.5 * diameter = 0.5 * 20 cm = 10 cm
height (h) = 8 cm
Using the values in the formula, we can calculate the volume of the cylinder: V_cylinder = π * (10 cm)^2 * 8 cm.

Now, add the volumes of the cone and cylinder together to get the total volume of the paperweight when it is empty: V_total = V_cone + V_cylinder.

To answer the second question, we need to find the height of the liquid in the cylinder when the paperweight is turned upside down and the liquid fills half the cylinder.

First, let's calculate the volume of the cylinder that will be filled by the liquid when it is half full. Half of the cylinder's volume can be calculated as V_half_cylinder = (1/2) * V_cylinder.

Next, we can use the known volume of the cone to calculate the equivalent height in the cylinder. By subtracting the volume of the cone from the volume of the half-filled cylinder, we can find the remaining liquid volume in the cylinder. We can then use the formula for the volume of a cylinder to calculate the height of the liquid in the cylinder: V_liquid = V_half_cylinder - V_cone and h_liquid = V_liquid / (π * r^2).

Using these steps, you can calculate the total volume of the paperweight when it is empty and determine the height of the liquid in the cylinder when the paperweight is turned upside down.