Let’s solve each problem one by one, step by step.
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Problem 1:
*If the length of a rectangular solid is unchanged but the width and height are tripled, then the volume of the original figure is multiplied by a factor of...*
Volume of a rectangular solid = length × width × height
Let original dimensions be:
- Length = L
- Width = W
- Height = H
→ Original Volume = L × W × H
Now, new dimensions:
- Length = L (unchanged)
- Width = 3W
- Height = 3H
→ New Volume = L × 3W × 3H = L × W × H × 9
So, new volume = 9 × original volume → multiplied by
9
✔ Answer for #1:
(d) 9
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Problem 2:
*A side of a cube measures 4 centimeters and a side of a smaller cube measures 2 centimeters. The volume of the larger cube is how many times the volume of the smaller cube?*
Volume of a cube = side³
Larger cube: side = 4 cm → Volume = 4³ = 64 cm³
Smaller cube: side = 2 cm → Volume = 2³ = 8 cm³
How many times bigger? → 64 ÷ 8 =
8
✔ Answer for #2:
(b) 8
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Problem 3:
*If the edge of a cube is 5 cm and the edge of a second cube is 2 cm, then the difference in the volumes of these cubes is...*
First cube: 5³ = 125 cm³
Second cube: 2³ = 8 cm³
Difference = 125 - 8 =
117 cm³
✔ Answer for #3:
(a) 117 cm³
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Problem 4:
*If the edge of a cube is doubled, the volume is multiplied by...*
Original edge = s → Volume = s³
New edge = 2s → New Volume = (2s)³ = 8s³
So, volume is multiplied by
8
✔ Answer for #4:
(c) 8
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Final Answer:
1) d
2) b
3) a
4) c
Parent Tip: Review the logic above to help your child master the concept of changing dimensions perimeter and area worksheet.
