Scaling every edge scales the volume three times over
7.G.A.16.G.A.2
Generated variants — 12
If every edge of the cube at the right is made five times in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all made five times. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 2 cm edges.
- Every edge is multiplied by 5.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 5 grows by the same 125, because the 2s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is tripled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all tripled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 3 cm edges.
- Every edge is multiplied by 3.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 3 grows by the same 27, because the 3s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is doubled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all doubled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 4 cm edges.
- Every edge is multiplied by 2.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 2 grows by the same 8, because the 4s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is doubled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all doubled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 5 cm edges.
- Every edge is multiplied by 2.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 2 grows by the same 8, because the 5s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is quadrupled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all quadrupled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 6 cm edges.
- Every edge is multiplied by 4.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 4 grows by the same 64, because the 6s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is tripled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all tripled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 7 cm edges.
- Every edge is multiplied by 3.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 3 grows by the same 27, because the 7s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is doubled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all doubled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 8 cm edges.
- Every edge is multiplied by 2.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 2 grows by the same 8, because the 8s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is quadrupled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all quadrupled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 9 cm edges.
- Every edge is multiplied by 4.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 4 grows by the same 64, because the 9s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is tripled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all tripled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 10 cm edges.
- Every edge is multiplied by 3.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 3 grows by the same 27, because the 10s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is doubled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all doubled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 12 cm edges.
- Every edge is multiplied by 2.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 2 grows by the same 8, because the 12s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is made five times in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all made five times. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 15 cm edges.
- Every edge is multiplied by 5.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 5 grows by the same 125, because the 15s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
If every edge of the cube at the right is quadrupled in length, the new cube's volume is how many times the original cube's volume?
Show solution
1 · Understandwhat's really being asked
A cube's edges are all quadrupled. We want how many times bigger the new volume is than the old.
Givens
- The original cube has 20 cm edges.
- Every edge is multiplied by 4.
Unknowns
- How many times the volume grows.
Constraints
- All three edges change by the same factor, so the shape stays a cube.
2 · Planchoose the strategy
#9 Solve an Easier Related Problem
Volume is three lengths multiplied together, so ask what happens to a product when every factor grows. The starting edge is there to check the answer with, not to reach it.
3 · Execute3 carry out the plan
1Write the old volume
2Scale every edge
3Compare the two
4 · Reviewdoes it hold up?
The starting edge never mattered: any cube scaled by 4 grows by the same 64, because the 20s cancel in the division.
Standardsmin grade 7
7.G.A.1Solve problems involving scale drawings of geometric figures — Reading what scaling every length does to the solid.6.G.A.2Volume of right rectangular prisms with fractional edges — Computing a cube's volume from its edge.
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