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All courses Geometry · G-MG.1 52 of 57
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 \(\text{single}~\text{geometric}~\text{solid}\) could you use to approximate this object: basketball?
Prompt illustration of the basketball alone, without naming its ideal geometric solid. Open full size
Your answer
Show answer choicesHide answer choices Work through the mathematics first, then compare your reasoning.Select the answer that matches your work.
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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

Identify the whole object

\[\text{object}=\text{basketball}\]

The prompt asks for one solid that models the basketball as a whole, not its seams or surface pattern.

02

Compare dimensions

\[\text{width}~\text{approx}~\text{height}~\text{approx}~\text{depth}\]

A basketball extends about equally from its center in every spatial direction.

03

Compare solid features

\[\text{round}~\text{in}~\text{every}~\text{direction};~\text{no}~\text{flat}~\text{faces};~\text{no}~\text{edges};~\text{no}~\text{taper}\]

These properties rule out cylinders, cones, prisms, and pyramids.

04

Choose the ideal solid

\[\text{sphere}\]

A sphere is the solid whose surface lies one radius from its center in every direction, matching the basketball's overall shape.

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Another way

  1. Imagine slicing the ball through its center in several directions; each central cross-section is approximately a circle of the same radius, which characterizes a sphere.

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Common mistake

Do not choose circle. A circle is two-dimensional, while the prompt asks for a solid that models the basketball's full three-dimensional shape.

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

Solution walkthrough video