Problem preview
G-GMD.3 Warmup M2-038-A06-V01

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

Find a missing radius from the volume of a cylinder, cone, or sphere

Problem

A cylinder has volume \(100~\pi\) and height \(4\). Find the missing radius.

Big Picture

What this problem is really about

The unknown radius is buried inside the circular base area, so solving for it requires two stages. We’ll substitute the known volume and height, divide away every factor outside the squared radius, take the square root only after that power is isolated, and keep the nonnegative value required by geometry.

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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 missing radius from the volume of a cylinder, cone, or sphere