Diameter is twice the radius
3.OA.C.73.G.A.1
Generated variants — 6
In the figure on the right, the diameter of the largest circle is . What is the radius of the smallest circle, in cm?
Show solution
1 · Understandwhat's really being asked
Three circles of different sizes sit on one horizontal line and all touch at one point on the left. The medium circle's diameter is the largest circle's radius, and the smallest circle's diameter is the medium circle's radius. The largest circle's diameter is 16 cm. We must find the radius of the smallest circle.
Givens
- The largest circle has diameter 16 cm.
- All three circles touch at the same single point on the left end, and their centers lie on one horizontal line.
- The medium circle's diameter equals the largest circle's radius.
- The smallest circle's diameter equals the medium circle's radius.
Unknowns
- The radius of the smallest circle in centimeters.
Constraints
- Diameter is always twice the radius, so a radius is half the diameter.
- Each smaller circle's diameter is the next larger circle's radius, so each circle inward is found from the one outside it.
2 · Planchoose the strategy
#1 Draw a Diagram
The picture shows each smaller circle reaching exactly to the center of the circle outside it, so each smaller diameter is the next larger radius. Work from the largest circle inward in three small steps, halving a diameter to get a radius each time.
3 · Execute3 carry out the plan
1Radius of the largest circle
2Radius of the medium circle
3Radius of the smallest circle
4 · Reviewdoes it hold up?
Going inward, each diameter is half the one before: 16 cm, 8 cm, 4 cm. The smallest radius is half of 4 cm, 2 cm. Checking backward: 2 x 2 = 4, 4 x 2 = 8, 8 x 2 = 16.
Standardsmin grade 3
3.G.A.1Understand that shapes in different categories share attributes — Using the diameter = twice the radius relationship for each circle.3.OA.C.7Fluently multiply and divide within 100 — Halving within 100 (16 -> 8 -> 4 -> 2).
In the figure on the right, the diameter of the largest circle is . What is the radius of the smallest circle, in cm?
Show solution
1 · Understandwhat's really being asked
Three circles of different sizes sit on one horizontal line and all touch at one point on the left. The medium circle's diameter is the largest circle's radius, and the smallest circle's diameter is the medium circle's radius. The largest circle's diameter is 24 cm. We must find the radius of the smallest circle.
Givens
- The largest circle has diameter 24 cm.
- All three circles touch at the same single point on the left end, and their centers lie on one horizontal line.
- The medium circle's diameter equals the largest circle's radius.
- The smallest circle's diameter equals the medium circle's radius.
Unknowns
- The radius of the smallest circle in centimeters.
Constraints
- Diameter is always twice the radius, so a radius is half the diameter.
- Each smaller circle's diameter is the next larger circle's radius, so each circle inward is found from the one outside it.
2 · Planchoose the strategy
#1 Draw a Diagram
The picture shows each smaller circle reaching exactly to the center of the circle outside it, so each smaller diameter is the next larger radius. Work from the largest circle inward in three small steps, halving a diameter to get a radius each time.
3 · Execute3 carry out the plan
1Radius of the largest circle
2Radius of the medium circle
3Radius of the smallest circle
4 · Reviewdoes it hold up?
Going inward, each diameter is half the one before: 24 cm, 12 cm, 6 cm. The smallest radius is half of 6 cm, 3 cm. Checking backward: 3 x 2 = 6, 6 x 2 = 12, 12 x 2 = 24.
Standardsmin grade 3
3.G.A.1Understand that shapes in different categories share attributes — Using the diameter = twice the radius relationship for each circle.3.OA.C.7Fluently multiply and divide within 100 — Halving within 100 (24 -> 12 -> 6 -> 3).
In the figure on the right, the diameter of the largest circle is . What is the radius of the smallest circle, in cm?
Show solution
1 · Understandwhat's really being asked
Three circles of different sizes sit on one horizontal line and all touch at one point on the left. The medium circle's diameter is the largest circle's radius, and the smallest circle's diameter is the medium circle's radius. The largest circle's diameter is 40 cm. We must find the radius of the smallest circle.
Givens
- The largest circle has diameter 40 cm.
- All three circles touch at the same single point on the left end, and their centers lie on one horizontal line.
- The medium circle's diameter equals the largest circle's radius.
- The smallest circle's diameter equals the medium circle's radius.
Unknowns
- The radius of the smallest circle in centimeters.
Constraints
- Diameter is always twice the radius, so a radius is half the diameter.
- Each smaller circle's diameter is the next larger circle's radius, so each circle inward is found from the one outside it.
2 · Planchoose the strategy
#1 Draw a Diagram
The picture shows each smaller circle reaching exactly to the center of the circle outside it, so each smaller diameter is the next larger radius. Work from the largest circle inward in three small steps, halving a diameter to get a radius each time.
3 · Execute3 carry out the plan
1Radius of the largest circle
2Radius of the medium circle
3Radius of the smallest circle
4 · Reviewdoes it hold up?
Going inward, each diameter is half the one before: 40 cm, 20 cm, 10 cm. The smallest radius is half of 10 cm, 5 cm. Checking backward: 5 x 2 = 10, 10 x 2 = 20, 20 x 2 = 40.
Standardsmin grade 3
3.G.A.1Understand that shapes in different categories share attributes — Using the diameter = twice the radius relationship for each circle.3.OA.C.7Fluently multiply and divide within 100 — Halving within 100 (40 -> 20 -> 10 -> 5).
In the figure on the right, the diameter of the largest circle is . What is the radius of the smallest circle, in cm?
Show solution
1 · Understandwhat's really being asked
Three circles of different sizes sit on one horizontal line and all touch at one point on the left. The medium circle's diameter is the largest circle's radius, and the smallest circle's diameter is the medium circle's radius. The largest circle's diameter is 48 cm. We must find the radius of the smallest circle.
Givens
- The largest circle has diameter 48 cm.
- All three circles touch at the same single point on the left end, and their centers lie on one horizontal line.
- The medium circle's diameter equals the largest circle's radius.
- The smallest circle's diameter equals the medium circle's radius.
Unknowns
- The radius of the smallest circle in centimeters.
Constraints
- Diameter is always twice the radius, so a radius is half the diameter.
- Each smaller circle's diameter is the next larger circle's radius, so each circle inward is found from the one outside it.
2 · Planchoose the strategy
#1 Draw a Diagram
The picture shows each smaller circle reaching exactly to the center of the circle outside it, so each smaller diameter is the next larger radius. Work from the largest circle inward in three small steps, halving a diameter to get a radius each time.
3 · Execute3 carry out the plan
1Radius of the largest circle
2Radius of the medium circle
3Radius of the smallest circle
4 · Reviewdoes it hold up?
Going inward, each diameter is half the one before: 48 cm, 24 cm, 12 cm. The smallest radius is half of 12 cm, 6 cm. Checking backward: 6 x 2 = 12, 12 x 2 = 24, 24 x 2 = 48.
Standardsmin grade 3
3.G.A.1Understand that shapes in different categories share attributes — Using the diameter = twice the radius relationship for each circle.3.OA.C.7Fluently multiply and divide within 100 — Halving within 100 (48 -> 24 -> 12 -> 6).
In the figure on the right, the diameter of the largest circle is . What is the radius of the smallest circle, in cm?
Show solution
1 · Understandwhat's really being asked
Three circles of different sizes sit on one horizontal line and all touch at one point on the left. The medium circle's diameter is the largest circle's radius, and the smallest circle's diameter is the medium circle's radius. The largest circle's diameter is 80 cm. We must find the radius of the smallest circle.
Givens
- The largest circle has diameter 80 cm.
- All three circles touch at the same single point on the left end, and their centers lie on one horizontal line.
- The medium circle's diameter equals the largest circle's radius.
- The smallest circle's diameter equals the medium circle's radius.
Unknowns
- The radius of the smallest circle in centimeters.
Constraints
- Diameter is always twice the radius, so a radius is half the diameter.
- Each smaller circle's diameter is the next larger circle's radius, so each circle inward is found from the one outside it.
2 · Planchoose the strategy
#1 Draw a Diagram
The picture shows each smaller circle reaching exactly to the center of the circle outside it, so each smaller diameter is the next larger radius. Work from the largest circle inward in three small steps, halving a diameter to get a radius each time.
3 · Execute3 carry out the plan
1Radius of the largest circle
2Radius of the medium circle
3Radius of the smallest circle
4 · Reviewdoes it hold up?
Going inward, each diameter is half the one before: 80 cm, 40 cm, 20 cm. The smallest radius is half of 20 cm, 10 cm. Checking backward: 10 x 2 = 20, 20 x 2 = 40, 40 x 2 = 80.
Standardsmin grade 3
3.G.A.1Understand that shapes in different categories share attributes — Using the diameter = twice the radius relationship for each circle.3.OA.C.7Fluently multiply and divide within 100 — Halving within 100 (80 -> 40 -> 20 -> 10).
In the figure on the right, the diameter of the largest circle is . What is the radius of the smallest circle, in cm?
Show solution
1 · Understandwhat's really being asked
Three circles of different sizes sit on one horizontal line and all touch at one point on the left. The medium circle's diameter is the largest circle's radius, and the smallest circle's diameter is the medium circle's radius. The largest circle's diameter is 120 cm. We must find the radius of the smallest circle.
Givens
- The largest circle has diameter 120 cm.
- All three circles touch at the same single point on the left end, and their centers lie on one horizontal line.
- The medium circle's diameter equals the largest circle's radius.
- The smallest circle's diameter equals the medium circle's radius.
Unknowns
- The radius of the smallest circle in centimeters.
Constraints
- Diameter is always twice the radius, so a radius is half the diameter.
- Each smaller circle's diameter is the next larger circle's radius, so each circle inward is found from the one outside it.
2 · Planchoose the strategy
#1 Draw a Diagram
The picture shows each smaller circle reaching exactly to the center of the circle outside it, so each smaller diameter is the next larger radius. Work from the largest circle inward in three small steps, halving a diameter to get a radius each time.
3 · Execute3 carry out the plan
1Radius of the largest circle
2Radius of the medium circle
3Radius of the smallest circle
4 · Reviewdoes it hold up?
Going inward, each diameter is half the one before: 120 cm, 60 cm, 30 cm. The smallest radius is half of 30 cm, 15 cm. Checking backward: 15 x 2 = 30, 30 x 2 = 60, 60 x 2 = 120.
Standardsmin grade 3
3.G.A.1Understand that shapes in different categories share attributes — Using the diameter = twice the radius relationship for each circle.3.OA.C.7Fluently multiply and divide within 100 — Halving within 100 (120 -> 60 -> 30 -> 15).