EM - Using Shapes to Describe Everyday Objects Lesson

Using Shapes to Describe Everyday Objects

Many everyday objects can be described by common geometric shapes. For example, a tree trunk could easily be modeled by a cylinder. A box is a rectangular prism, a baseball is a sphere, and an ice cream cone is... you guessed it, a cone! The possibilities are endless when it comes to the relationships between everyday objects and geometric figures. Let's see what you know!

What geometric shape describes the cereal box on the left

Solution: Rectangular Prism

Let's assume the box has a height of 10 inches, a length of 8 inches, and a width of 2 inches. How much cereal can this box hold?

Since we know it is a rectangular prism, we can simply use the formula for the volume of a rectangular prism:

V = (length)(width)(height)

V = (8 inches)(2 inches)(10 inches)

V = 160 cubic inches

So the box can hold 160 cubic inches of cereal.

A standard basketball has a diameter of approximately 9.5 inches. How much air does it take to fill the basketball?

Let's figure it out...

First, since we are talking about filling the basketball, this means we want to find the volume .

To find the volume, we need to know what shape the basketball is.

Solution: sphere

Great! The volume of a sphere is represented by the formula $LaTeX: V=\frac{4}{3}\Pi r^3$ $V=\frac{4}{3}\Pi r^3$ . We know the diameter of the basketball is 9.5 inches, but we need the radius, which is half of the diameter. So the radius is 4.75 inches. Let's plug this in to our formula:

$LaTeX: V=\frac{4}{3}\Pi\left(4.75\right)^3$ $V=\frac{4}{3}\Pi\left(4.75\right)^3$ equation image indicator

V = 448.92 cubic inches

Thus, it will take approximately 448.92 cubic inches of air to fill the basketball.

These standard dice can be modeled by which geometric figure?

Solution: Cube

One die has a side length of 12 millimeters. What is the surface area of the die?

The die has 6 sides, all of equal size (since it is a cube).

The area of one side is 12 x 12 = 144 mm²

Multiply this by 6 to get the total surface area.

Solution: $LaTeX: 864\:mm^2$ $864\:mm^2$

Can you think of some other objects that you could describe using various geometric shapes? If nothing comes to mind, take a walk and keep your eyes peeled - you will definitely find some!

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