Practice
Prisms Practice
Fifty original questions on prism structure, surface area, volume, cubes, removed regions, density, open-top boxes, units, and water levels.
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Question 1
Explanation
A prism is defined by two congruent and parallel polygonal faces; those are its bases.
- Geometry and units
Use the structural definition, not the drawing's orientation.
Question 2
Explanation
Height is defined as perpendicular distance between the parallel base planes.
- Geometry and units
Look for a perpendicular relationship rather than apparent visual length.
Question 3
Explanation
A prism extends a base area B through perpendicular height h, so V=Bh.
- Geometry and units
Volume uses base area, not base perimeter.
Question 4
Explanation
Unfolding the lateral faces makes a strip with total width P and height h, so LA=Ph.
- Geometry and units
Lateral area uses perimeter because the strip wraps around the base.
Question 5
Explanation
The lateral faces contribute Ph and the two congruent bases contribute 2B.
- Geometry and units
Count exposed surfaces: lateral strip plus base 1 plus base 2.
Question 6
Explanation
Choose a rectangular base of area 8·5=40 cm² and multiply by height 3: V=120 cm³.
- Geometry and units
Multiply three perpendicular dimensions and report cubic units.
Question 7
Explanation
Choose a rectangular base of area 11·6=66 cm² and multiply by height 4: V=264 cm³.
- Geometry and units
Multiply three perpendicular dimensions and report cubic units.
Question 8
Explanation
Choose a rectangular base of area 14·7=98 cm² and multiply by height 5: V=490 cm³.
- Geometry and units
Multiply three perpendicular dimensions and report cubic units.
Question 9
Explanation
Choose a rectangular base of area 9·8=72 cm² and multiply by height 6: V=432 cm³.
- Geometry and units
Multiply three perpendicular dimensions and report cubic units.
Question 10
Explanation
Choose a rectangular base of area 15·4=60 cm² and multiply by height 9: V=540 cm³.
- Geometry and units
Multiply three perpendicular dimensions and report cubic units.
Question 11
Explanation
Six square faces each have area 2²=4; SA=6(4)=24 in².
- Geometry and units
Surface area uses six s-squared faces.
Question 12
Explanation
Cube volume is s³=3³=27 in³.
- Geometry and units
Volume uses the third power of edge length.
Question 13
Explanation
Six square faces each have area 4²=16; SA=6(16)=96 in².
- Geometry and units
Surface area uses six s-squared faces.
Question 14
Explanation
Cube volume is s³=5³=125 in³.
- Geometry and units
Volume uses the third power of edge length.
Question 15
Explanation
Six square faces each have area 6²=36; SA=6(36)=216 in².
- Geometry and units
Surface area uses six s-squared faces.
Question 16
Explanation
LA=Ph=(36)(7)=252 cm².
- Geometry and units
Use base perimeter for lateral area.
Question 17
Explanation
LA=Ph=(26)(9)=234 cm².
- Geometry and units
Use base perimeter for lateral area.
Question 18
Explanation
TA=Ph+2B=(42)(5)+2(18)=246 cm².
- Geometry and units
Add both congruent base areas to the lateral strip.
Question 19
Explanation
TA=Ph+2B=(30)(8)+2(12)=264 cm².
- Geometry and units
Add both congruent base areas to the lateral strip.
Question 20
Explanation
TA=Ph+2B=(48)(6)+2(15)=318 cm².
- Geometry and units
Add both congruent base areas to the lateral strip.
Question 21
Explanation
The triangular base area is 1/2(6)(8)=24 m². Then V=Bh=(24)(11)=264 m³.
- Geometry and units
Calculate the triangle area before multiplying by the separate prism height.
Question 22
Explanation
The triangular base area is 1/2(10)(7)=35 m². Then V=Bh=(35)(9)=315 m³.
- Geometry and units
Calculate the triangle area before multiplying by the separate prism height.
Question 23
Explanation
The triangular base area is 1/2(12)(5)=30 m². Then V=Bh=(30)(14)=420 m³.
- Geometry and units
Calculate the triangle area before multiplying by the separate prism height.
Question 24
Explanation
The triangular base area is 1/2(9)(8)=36 m². Then V=Bh=(36)(13)=468 m³.
- Geometry and units
Calculate the triangle area before multiplying by the separate prism height.
Question 25
Explanation
The triangular base area is 1/2(16)(6)=48 m². Then V=Bh=(48)(7)=336 m³.
- Geometry and units
Calculate the triangle area before multiplying by the separate prism height.
Question 26
Explanation
V=Bh=(24)(7)=168.
- Geometry and units
Keep base area in square units while the missing height remains a length.
Question 27
Explanation
V=Bh=(35)(6)=210.
- Geometry and units
Keep base area in square units while the missing height remains a length.
Question 28
Explanation
V=Bh=(48)(5)=240.
- Geometry and units
Keep base area in square units while the missing height remains a length.
Question 29
Explanation
Solve h=V/B=432/54=8.
- Geometry and units
Keep base area in square units while the missing height remains a length.
Question 30
Explanation
Solve h=V/B=252/63=4.
- Geometry and units
Keep base area in square units while the missing height remains a length.
Question 31
Explanation
Outer volume is 24·15·8=2880. The through-opening is 5·4·8=160. Remaining volume is 2880-160=2720 cubic units.
- Geometry and units
Subtract the complete three-dimensional opening; do not subtract only its top area.
Question 32
Explanation
Outer volume is 30·18·7=3780. The through-opening is 6·3·7=126. Remaining volume is 3780-126=3654 cubic units.
- Geometry and units
Subtract the complete three-dimensional opening; do not subtract only its top area.
Question 33
Explanation
Outer volume is 20·16·10=3200. The through-opening is 4·5·10=200. Remaining volume is 3200-200=3000 cubic units.
- Geometry and units
Subtract the complete three-dimensional opening; do not subtract only its top area.
Question 34
Explanation
Outer volume is 28·14·9=3528. The through-opening is 7·2·9=126. Remaining volume is 3528-126=3402 cubic units.
- Geometry and units
Subtract the complete three-dimensional opening; do not subtract only its top area.
Question 35
Explanation
Outer volume is 32·20·6=3840. The through-opening is 8·5·6=240. Remaining volume is 3840-240=3600 cubic units.
- Geometry and units
Subtract the complete three-dimensional opening; do not subtract only its top area.
Question 36
Explanation
Mass=density·volume=(2.5)(480)=1200 g; cm³ cancels.
- Geometry and units
Check that density and volume use matching cubic units.
Question 37
Explanation
Mass=density·volume=(1.8)(720)=1296 g; cm³ cancels.
- Geometry and units
Check that density and volume use matching cubic units.
Question 38
Explanation
Mass=density·volume=(0.75)(960)=720 g; cm³ cancels.
- Geometry and units
Check that density and volume use matching cubic units.
Question 39
Explanation
Because 1 ft=12 in, cube the factor: 1 ft³=1·12³=1728 in³.
- Geometry and units
Cubic conversion factors are the cube of linear factors.
Question 40
Explanation
Because 1 ft=12 in, cube the factor: 3 ft³=3·12³=5184 in³.
- Geometry and units
Cubic conversion factors are the cube of linear factors.
Question 41
Explanation
The box height is 2. Its base is (22-2·2) by (16-2·2)=18 by 12. Thus V=18·12·2=432 in³.
- Geometry and units
Subtract two cut widths from both sheet dimensions, then multiply by cut height.
Question 42
Explanation
The box height is 3. Its base is (26-2·3) by (18-2·3)=20 by 12. Thus V=20·12·3=720 in³.
- Geometry and units
Subtract two cut widths from both sheet dimensions, then multiply by cut height.
Question 43
Explanation
The box height is 4. Its base is (30-2·4) by (20-2·4)=22 by 12. Thus V=22·12·4=1056 in³.
- Geometry and units
Subtract two cut widths from both sheet dimensions, then multiply by cut height.
Question 44
Explanation
The box height is 2. Its base is (24-2·2) by (14-2·2)=20 by 10. Thus V=20·10·2=400 in³.
- Geometry and units
Subtract two cut widths from both sheet dimensions, then multiply by cut height.
Question 45
Explanation
The box height is 5. Its base is (28-2·5) by (22-2·5)=18 by 12. Thus V=18·12·5=1080 in³.
- Geometry and units
Subtract two cut widths from both sheet dimensions, then multiply by cut height.
Question 46
Explanation
Water depth is V/B=960/120=8 cm. The requested gap is 14-8=6 cm.
- Geometry and units
Separate water depth from distance below the tank top.
Question 47
Explanation
Water depth is V/B=1650/150=11 cm. The requested gap is 16-11=5 cm.
- Geometry and units
Separate water depth from distance below the tank top.
Question 48
Explanation
Water depth is V/B=756/84=9 cm. The requested gap is 13-9=4 cm.
- Geometry and units
Separate water depth from distance below the tank top.
Question 49
Explanation
Water depth is V/B=2200/200=11 cm. The requested gap is 15-11=4 cm.
- Geometry and units
Separate water depth from distance below the tank top.
Question 50
Explanation
Water depth is V/B=1296/144=9 cm. The requested gap is 12-9=3 cm.
- Geometry and units
Separate water depth from distance below the tank top.
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Questions to review
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- Question 1Prism elementsEasy
- Question 2Prism heightEasy
- Question 3Prism volumeEasy
- Question 4Prism lateral areaEasy
- Question 5Prism total areaEasy
- Question 6Rectangular-prism volumeEasy
- Question 7Rectangular-prism volumeEasy
- Question 8Rectangular-prism volumeEasy
- Question 9Rectangular-prism volumeEasy
- Question 10Rectangular-prism volumeEasy
- Question 11Cube formulasEasy
- Question 12Cube formulasEasy
- Question 13Cube formulasEasy
- Question 14Cube formulasEasy
- Question 15Cube formulasEasy
- Question 16Lateral areaMedium
- Question 17Lateral areaMedium
- Question 18Total surface areaMedium
- Question 19Total surface areaMedium
- Question 20Total surface areaMedium
- Question 21Triangular-prism volumeMedium
- Question 22Triangular-prism volumeMedium
- Question 23Triangular-prism volumeMedium
- Question 24Triangular-prism volumeMedium
- Question 25Triangular-prism volumeMedium
- Question 26Prism reverse problemsMedium
- Question 27Prism reverse problemsMedium
- Question 28Prism reverse problemsMedium
- Question 29Prism reverse problemsMedium
- Question 30Prism reverse problemsMedium
- Question 31Removed volumeMedium
- Question 32Removed volumeMedium
- Question 33Removed volumeMedium
- Question 34Removed volumeMedium
- Question 35Removed volumeMedium
- Question 36DensityMedium
- Question 37DensityMedium
- Question 38DensityMedium
- Question 39Cubic-unit conversionMedium
- Question 40Cubic-unit conversionMedium
- Question 41Open-top boxesHard
- Question 42Open-top boxesHard
- Question 43Open-top boxesHard
- Question 44Open-top boxesHard
- Question 45Open-top boxesHard
- Question 46Water-level applicationsHard
- Question 47Water-level applicationsHard
- Question 48Water-level applicationsHard
- Question 49Water-level applicationsHard
- Question 50Water-level applicationsHard