I can find the volume of a rectangular prism with whole-number edges using length × width × height.Puedo hallar el volumen de un prisma rectangular con aristas de números enteros usando largo × ancho × altura.
MissionMisión · Case FilesExpedientes · night shiftturno de noche
Follow the numbers to the truth.Sigue los números hasta la verdad.
After midnight, the detective bureau finds a vault of unlabeled crates. Work out the volume of each crate before the morning briefing, because one of them holds the missing piece of the case.
Después de la medianoche, la oficina de detectives encuentra una bóveda con cajones sin etiquetar. Calcula el volumen de cada cajón antes de la reunión de la mañana, porque uno de ellos guarda la pieza que falta del caso.
Word bankBanco de palabras 4 words4 palabrasvolume, rectangular prism, cubic units, …volumen, prisma rectangular, unidades cúbicas, …
- volumevolumen
- How much space is inside a solid shape, counted in unit cubes.Cuánto espacio hay dentro de una figura sólida, contado en cubos unitarios.
- rectangular prismprisma rectangular
- A solid box shape with six flat rectangle sides.Una figura sólida en forma de caja con seis lados rectangulares.
- cubic unitsunidades cúbicas
- The units used to measure the space inside, like cubic inches (in³).Las unidades para medir el espacio interior, como pulgadas cúbicas (pulg³).
- edgearista
- The line where two flat sides of a solid meet.La línea donde se unen dos lados planos de un sólido.
Stage 1 of 5Etapa 1 de 5
Start StrongEmpieza fuerte
Each rung is harder than the last, and the numbers change every time.
Cada peldaño es más difícil que el anterior y los números cambian cada vez.
- 6 fresh problems with new numbers each time (interactive only).
Stage 2 of 5Etapa 2 de 5
Stretch Your ThinkingAmplía tu pensamiento
Plan, solve, then check that your answer makes sense.
Planea, resuelve y revisa que tu respuesta tenga sentido.
- Find the Volume Error
- A box needs to hold exactly 60 cubic inches. Give three different sets of whole-number dimensions that work. Which set would make the box closest to a cube shape? Why might that matter?
- Fill in the table
- Detective Reyes is packing 1-inch evidence cubes into a box that is 12 in long, 5 in wide and 4 in tall. She has 200 cubes. How many more cubes does she need to fill the box?
- Three lockers hold evidence. Locker A is 6 in by 5 in by 10 in. Locker B is 8 in by 6 in by 7 in. Locker C is 9 in by 4 in by 9 in. Which locker holds the most?
- Locker A, because it is the tallest
- Locker B, 336 in³
- Locker C, because it has the biggest base
- They all hold the same
- Four evidence crates are rectangular prisms. Find each missing value. Type numbers only.
- A vault is a rectangular prism 6 ft long, 4 ft wide and 5 ft tall. A bigger vault has every edge twice as long. How many times as much does the bigger vault hold?
- 2 times as much
- 4 times as much
- 6 times as much
- 8 times as much
Stage 3 of 5Etapa 3 de 5
InvestigateInvestiga
Use the model to test an idea. Then check it.
Usa el modelo para probar una idea. Luego compruébala.
- The detectives label every measurement in the case. Sort each unit by what it measures.
- Design a rectangular box that holds exactly 48 unit cubes. Give its length, width and height and show base area × height. Then design a second box with different edges and the same volume. Explain why both boxes hold the same.
- 4 fresh problems with new numbers each time (interactive only).
Stage 4 of 5Etapa 4 de 5
Find and FixEncuentra y corrige
Somebody made a mistake. Find the step and fix it.
Alguien cometió un error. Encuentra el paso y corrígelo.
- An evidence box is 5 in long, 3 in wide and 4 in tall. Carla finds its volume. Tap the first step where her work goes wrong.
- A crate is 4 ft long, 3 ft wide and 5 ft tall. Hugo finds its volume. Tap the first step where his work goes wrong.
- A case box is 11 in long, 5 in wide and 4 in tall. Jules finds its volume. Tap the first step where his work goes wrong.
- Box P is 2 in by 6 in by 6 in. Box Q is 3 in by 4 in by 6 in. Tomás says Box P holds more because it has two long edges. Lin says they hold the same amount. Who is right?
- Tomás, because longer edges mean more volume.
- Neither. Box Q holds more because it has more different edges.
- Neither. Box P holds more, because its 6 in by 6 in face is the biggest face.
- Lin. Both boxes have a volume of 72 in³.
- What is the best next move?
- Divide 180 by the base area, 6 × 5.
- Subtract 6 and 5 from 180.
- Multiply 180 by 6 and by 5.
- Divide 180 by 6 and call that the height.
Stage 5 of 5Etapa 5 de 5
Prove Your UnderstandingDemuestra tu comprensión
Say how sure you are, solve, then create a problem of your own.
Di qué tan seguro estás, resuelve y luego crea un problema tuyo.
- A rectangular prism evidence tank is 11 cm long, 6 cm wide and 3 cm tall. What is its volume, in cubic centimeters?
- A box is 7 cm long, 4 cm wide and 5 cm tall. Which answer has the correct number and unit for its volume?
- 140 cm³
- 140 cm²
- 16 cm³
- 28 cm³
- A storage trunk has a volume of 150 in³. Its base is 10 in by 5 in. What is the height of the trunk, in inches?
- Four crates have these edges: 3 × 3 × 3, 10 × 2 × 2, 5 × 4 × 3 and 6 × 6 × 2 (all in feet). Which crate holds the least?
- 10 × 2 × 2
- 3 × 3 × 3
- 5 × 4 × 3
- 6 × 6 × 2
- Nia fills a box that is 8 in long, 5 in wide and 3 in tall with 1-inch evidence cubes. The cubes come in bags of 24. How many bags does she need?
- Create your own Case Files problem about the volume of a box. Give the length, width and height, find the volume, and explain why the answer uses cubic units.