One turn of a wheel covers exactly one circumference
7.G.B.4
Generated variants — 12
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 10 cm rolls 10.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 10 cm.
- It makes 10.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
659.4 cm is between 596.6 and 722.2 -- between what 9.5 and 11.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 12 cm rolls 8.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 12 cm.
- It makes 8.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
640.56 cm is between 565.2 and 715.92 -- between what 7.5 and 9.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 15 cm rolls 6.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 15 cm.
- It makes 6.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
612.3 cm is between 518.1 and 706.5 -- between what 5.5 and 7.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 20 cm rolls 3.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 20 cm.
- It makes 3.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
439.6 cm is between 314 and 565.2 -- between what 2.5 and 4.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 25 cm rolls 2.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 25 cm.
- It makes 2.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
392.5 cm is between 235.5 and 549.5 -- between what 1.5 and 3.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 28 cm rolls 4.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 28 cm.
- It makes 4.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
791.28 cm is between 615.44 and 967.12 -- between what 3.5 and 5.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 30 cm rolls 4.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 30 cm.
- It makes 4.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
847.8 cm is between 659.4 and 1036.2 -- between what 3.5 and 5.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 35 cm rolls 7.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 35 cm.
- It makes 7.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
1648.5 cm is between 1428.7 and 1868.3 -- between what 6.5 and 8.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 40 cm rolls 5.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 40 cm.
- It makes 5.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
1381.6 cm is between 1130.4 and 1632.8 -- between what 4.5 and 6.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 45 cm rolls 3.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 45 cm.
- It makes 3.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
989.1 cm is between 706.5 and 1271.7 -- between what 2.5 and 4.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 50 cm rolls 1.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 50 cm.
- It makes 1.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
471 cm is between 157 and 785 -- between what 0.5 and 2.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
A hoop with a radius of is rolled in one direction and makes and a half turns. How far does it travel, in ?
Show solution
1 · Understandwhat's really being asked
A hoop of radius 60 cm rolls 2.5 turns without slipping. We want the distance it covers.
Givens
- The hoop's radius is 60 cm.
- It makes 2.5 turns.
Unknowns
- The distance the hoop travels.
Constraints
- It rolls without slipping, so the rim lays itself out along the ground.
2 · Planchoose the strategy
#17 Visualize Spatial Relationships
Picture one turn: every point of the rim touches the ground exactly once, so the hoop moves forward by its own circumference. After that the distance is one multiplication.
3 · Execute3 carry out the plan
1Find the circumference
2See what one turn covers
3Multiply by the turns
4 · Reviewdoes it hold up?
942 cm is between 565.2 and 1318.8 -- between what 1.5 and 3.5 turns would give, as it must be.
Standardsmin grade 7
7.G.B.4Know the formulas for area and circumference of a circle — Finding the circumference and using it as the distance per turn.
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