Back to Use shapes to describe objects — Problem 1 · Task Set 41

Exercises: Use Geometric Shapes to Describe Objects

Work through each section in order. When you choose a geometric model, say what shape
you picked and why. Use $\pi \approx 3.14159$ and round as each problem directs.

Grade 10·23 problems·~35 min·Common Core Math - HS Geometry·standard·hsg-mg-a-1

Work through problems with immediate feedback

Fluency Practice

$Side view of a water bottle divided into a straight body, a narrower straight neck, and a rounded top, shown beside a tall cylinder, a short cylinder, and a half-sphere$

A plastic water bottle has a straight-sided body, a narrower straight neck above it, and a rounded dome cap on top. Which set of shapes models the bottle, part by part, with the fewest pieces that still capture all three sections?

One cylinder for the whole bottle, since the bottle is taller than it is wide and a single shape is always the simplest choice available.

A cylinder for the body, a narrower cylinder for the neck, and a hemisphere for the cap.

A cylinder for the body, a cone for the neck, and a hemisphere for the cap, because the neck is narrower than the body and a cone is the shape that narrows.

A rectangular prism for the body, a narrower rectangular prism for the neck, and a pyramid for the cap, since prisms and pyramids have the flat faces a manufactured container needs.