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G-GMD.3 Warmup M2-038-A07-V02

Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.

Compare two exact solid volumes by relation, ratio, and difference

Problem

Solid A is a sphere of radius \(3\); solid B is a cylinder of radius \(3\) and height \(4\). Calculate \(\text{both}~\text{exact}~\text{volumes}\), then state their relation, the simplified ratio \(A:B\), and the signed difference \(A~-~B\).

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Solid A has three-fourths the volume of solid B.

Solid A has three times the volume of solid B.

Solid A has four-thirds the volume of solid B.

VA=4/3·π·3³=36π and VB=π·3²·4=36π cubic units; the volumes are equal, A:B=1:1, and A−B=0.

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Curriculum context

Course: Math II
Standard: G-GMD.3
Category: Geometry
Domain: Geometric Measurement and Dimension
Objective: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
Problem type: Compare two exact solid volumes by relation, ratio, and difference