Thread: Geometry Problems

I have two questions that I've been stuck on for a very long time and need any help I can get!

1. A certain tower has a mass of 7.2 million kilograms and a height of 324 meters. Its base is square with a side length of 125 meters. The steel used to make the tower occupies a volume of 930 cubic meters. Air has a density of 1.225 kg per cubic meter. Suppose the tower was contained in a cylinder. Find the mass of the air in the cylinder. (Assume the dimensions of the cylinder minimize the volume. Round your answer to three decimal places.)

I know the answer should be __ million kg.

2. Aleko's Pizza has delivered a beautiful 18 inch diameter pie to Lee's dorm room. The pie is sliced into 8 equal sized pieces, but Lee is such a non-conformist he cuts off an edge as pictured. John then takes one of the remaining triangular slices.



Who has more pizza and by how much? (Round your answer to two decimal places.)

I know Lee should have more I just need help finding how much.


Again, any help with how to solve these is appreciated! Thank you very much!

Hey Phresh.

First off, do you know the formula for the area of a triangle (with ones that include right angles) and also the formula for a portion of a circle with a given radius and a known arc?

Originally Posted by chiro

Hey Phresh.

First off, do you know the formula for the area of a triangle (with ones that include right angles) and also the formula for a portion of a circle with a given radius and a known arc?

I've been applying the formula for right triangles to both problems but I just can't get the right answer to any of them. And no I don't for the circle with a given radius and known arc.

The area for a portion of a circle is (1/2)*r^2*theta where theta is the angular interval measure. So for example a quarter of a circle has theta = pi/2 and a full revolution is 2*pi which if you plug in gives the area of a circle to be 1/2*2*pi*r^2 = pi*r^2.

So if you have triangles pi/4 radians each then the total arc corresponds to a pi/2 angular measure.