Modeling with Geometry - Geometry

In the world around us, all figures can be looked at in geometric shapes.

Looking at the three-dimensional open box,

two figure can be broken down into two main shapes, one which is a three-dimensional shape and the other is a two-dimensional shape. The box itself can be described as a rectangular prism. The lid of the box, which is up and thus making the box open is a rectangle.

In the three-dimensional world a coffee mug without a handle has a bottom and top in the shape of a circle. The three-dimensional connection between the top and the bottom creates a cylinder. Therefore, the geometric shape that best describes the coffee mug is an open cylinder since there is no top on the coffee mug.

A basketball hoop is constructed of a pole, a backboard, a rim, and a net that is attached to the rim. Since the question is asking for the geometric shape that describes the rim, recall that the rim of the basketball hoop has the geometric shape of a circle.

The goal of this problem is to find the surface area of the triangular prism and see if you have enough 1in x 1in stamps to fill the surface area without leaving any open gaps. To find the surface area of the prism we know that there are two triangular faces, and three rectangular faces. We will find the area of each of these and then their sum is the total surface area.

Area for each triangular face:

Area for each rectangular face:

So now we will sum 2 triangular faces and three rectangular faces for the total surface area.

Since we want to find if we have enough stamps, we will divide the total surface area by the surface area of an individual stamp to find how many stamps we would need to cover the prism entirely.

We only have 112 stamps, so we do not have enough stamps.

This is an area problem. For a fenced in, flat area, we would only consider the height and width. To be a volume problem we would need to have a 3-dimensional space to fill, one with width, length, and height.

The formula to find the volume of a cylinder is . While we have the volume of the bottle, we do not have the height. In order to work backwards to find the radius we would also need the height of the cylinder.

A box in three-dimensional space can be describes as either a cube or a rectangular prism depending on the side lengths. Since rectangular prism is the only option available, this is the best option. Most shoe boxes in general are rectangular prisms since shoes are longer than they are wide.

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is 9513.03 kilograms.

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume. Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .

In order to solve this problem, we need to use an equation that involves, density, mass, and volume.

Here is the equation that we need to use.

Since we are given the density, and volume, we can plug those values in, and then solve for the mass ().

Thus the mass of the balloon is .