Problem preview

G-MG.1 Warmup M3-039-A06-V02

Use geometric shapes, measurements, and properties to describe real-world objects.

Inventory surfaces and compute exact/two-decimal area

Problem

Use the diagram to inventory the exposed surfaces of an open-top cylinder with \(r~=~3\) and \(h~=~4\). Calculate the exact surface area in terms of \(\pi~\) and the area to \(\text{two}~\text{decimal}~\text{places}\) with \(\text{square}~\text{units}\).

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SA=2π(3)²+2π(3)(4)=42π units², or 131.95 units², counting the open top.

V=π(3)²(4)=36π units³, or 113.10 units³, a volume.

SA=π(3)²+2π(3)(4)=33π units², or 103.67 units².

SA=33(3)=99 units², using π=3 before the final rounding.

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Curriculum context

Course: Math III
Standard: G-MG.1
Category: Geometry
Domain: Modeling with Geometry
Objective: Use geometric shapes, measurements, and properties to describe real-world objects.
Problem type: Inventory surfaces and compute exact/two-decimal area