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All courses Math III · G-MG.1 39 of 55
Use geometric shapes, measurements, and properties to describe real-world objects.

Choose the best single solid model for a real-world object from sphere, cylinder, cone, prism, or pyramid

Problem
What single geometric solid could you use to approximate this object: basketball?
Prompt illustration of the basketball alone, without naming its ideal geometric solid. Open full size
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Hint

Think about whether the object is equally round in every direction or has flat faces.

A sphere is the best model for an object that is round in all directions with no edges or flat circular top and bottom.

Solution walkthrough

01

Notice the overall shape

\[\text{basketball}\]

A basketball is round all the way around rather than having flat ends or a pointed tip.

02

Compare to common solids

\[\text{not cylinder, not cone}\]

A cylinder has two flat circular bases, and a cone has one circular base and a point, so neither matches a basketball.

03

Choose the best geometric model

\[\text{sphere}\]

A sphere matches an object that is curved in every direction.

04

State the approximation

\[\text{solid: sphere}\]

So a sphere is the single geometric solid that best approximates a basketball.

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Another way

  1. You can imagine slicing the object through its center in any direction; a basketball stays circular, which is a strong clue for a sphere.

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Common mistake

A common mistake is choosing a cylinder because both have circular views from some angles, but a cylinder has flat ends while a basketball does not.

Answer comparison of the basketball and its role-correct sphere model with matched features labeled.