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Math / Geometry / Grade 5 / mg502

Build Volume One Layer at a Time

Count cubic units in rectangular prisms and use layers to find missing dimensions.

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Find how many unit cubes fit in one layer: length x width. Multiply by the number of layers. Volume uses cubic units, not the square units used for area.

Worked example

A prism with a base 4 cm by 2 cm has eight cubic-centimeter cubes in each 1-cm-high layer. Three layers give 4 x 2 x 3 = 24 cubic cm.

Three separate rectangular layers each show a four-column, two-row array of eight unit cubes viewed from above. Eight cubes per layer times three layers gives twenty-four cubic centimeters.
These are three layers shown separately, not three different solids. Stack them to build a prism with volume twenty-four cubic centimeters.
Question 1 A box is 5 cm long, 3 cm wide and 2 cm high. What is its volume in cubic cm?
Question 2 A prism has a 4 cm by 4 cm base and is 3 cm high. What is its volume in cubic cm?
Question 3 A prism has volume 60 cubic cm and a base 5 cm by 4 cm. How high is it, in cm?
Question 4 A prism has 4 layers. Each layer has 2 rows of 3 unit cubes. How many unit cubes are there altogether?
Question 5 Two separate blocks each measure 3 cm by 2 cm by 2 cm. What is their combined volume in cubic cm?