Problem
The largest circle's diameter is 40 cm. Radius is half the diameter, so the largest radius is 20 cm.
Diameter is twice the radius, so halving the diameter gives the radius.
3.G.A.1Identify SubproblemsThe radius of the largest circle is half of its 40 cm diameter.
The diameter is two radii joined end to end at the center, so it measures two radius-lengths and taking half of it gives back one radius.
The center sits on the diameter and cuts it into two pieces, each reaching from the center out to the edge, and those two pieces fit together with no gap to make the whole diameter.
The two pieces are the same length, because folding the circle in half along the line through the center lays one piece exactly onto the other.
If the diameter is one radius doubled, then dividing the diameter by two undoes the doubling and returns a single radius.
The medium radius is 3/5 of the largest (60 next to 100): 20 ÷ 5 × 3 = 12 cm.
Reading the matching proportions in the picture lets a Grade 3 student scale the known radius down.
3.OA.C.7Draw A DiagramThe smallest radius is half the medium (30 next to 60): 12 ÷ 2 = 6 cm.
Half of the medium radius gives the smallest radius, a simple division within 100.
3.OA.C.7Draw A DiagramHalf a diameter is a radius -- keep halving and scaling with Grade 3 division and the smallest circle pops out!