Problem preview
G-GMD.3 Warmup M2-038-A05-V01

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

Find a solid's height from volume and base measure

Problem

Find the solid's height from cylinder volume \(V=90\pi~\text{cubic}~\text{units}\) and radius \(r=3~\text{units}\).

Big Picture

What this problem is really about

Because the unknown is a dimension rather than the volume, the cylinder relationship must be rearranged around the height. We’ll form the circular base area from the radius, divide the given volume by that entire area, simplify common factors, and verify both the original equation and the surviving linear units.

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Four variants of this problem type
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
Find a solid's height from volume and base measure