Problem preview
G-C.5 Warmup M2-033-A10-V01

Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.

Find a missing sector measure from the sector area formula in radians

Problem

A sector has \(A=25\pi\) and \(r=10\). Find the missing value.

Big Picture

What this problem is really about

The unknown is an angle, so we’ll use the radian sector-area formula and isolate that factor rather than treating the drawing as measured. We’ll square the radius, simplify the coefficient of the angle, divide the given area by it, and substitute back to verify the sector.

Inside Gozunta

Turn the preview into practice.

More than a preview

Gozunta lets you study this problem—and more than 10,000 others.

Create targeted learning sessions, use hints, check your answer, read the walkthrough, watch the video, print the work, and track your progress.

Discover Gozunta Try it now
Four variants of this problem type
Curriculum context
Course
Math II
Standard
G-C.5
Category
Geometry
Domain
Circles
Objective
Derive arc length and sector area formulas using similarity; define radians and convert degrees/radians.
Problem type
Find a missing sector measure from the sector area formula in radians