Problem
Radius is half the diameter. Large radius is 8 / 2 = 4 in; small radius is 5 / 2 = 2.5 in.
Diameter is twice the radius, so halving gives each radius.
3.G.A.1Draw A DiagramThe distance is large radius + small radius = 6.5 in.
Two radii laid end to end across the touch point give the distance between the two centers.
3.MD.D.8Identify SubproblemsWhen a large circle and a small circle touch on the outside, the distance between their two centers equals the large radius plus the small radius.
You can travel from the large center straight to the touch point and then straight on to the small center, and these two straight parts lie along one line with no gap or overlap between them.
The part from the large center to the touch point is exactly the large radius, because the touch point sits on the large circle and every point on a circle is exactly one radius from its center.
The part from the touch point to the small center is exactly the small radius, because that point sits on the small circle and every point on a circle is exactly one radius from its center.
Two straight parts that meet end to end with no gap or overlap add up to the whole straight distance between the two centers.
All four equal sides (6.5 in) mean the perimeter is 4 × 6.5 = 26 in.
All four sides are equal, so adding them is the same as multiplying one side by 4.
3.OA.C.7Identify SubproblemsEach side is a big radius plus a small radius -- add them, then multiply by 4 sides with Grade 3 math!