Question

Question Statement: In the figures shown, each cube has a volume of 1 cubic unit. Compare the volume $V$ (in cubic units) of each rectangular prism to the area $B$ (in square units) of its base. What do you notice?

Answer 1

Hint: Each cube has a volume of 1 cubic unit.

Step 1: Find edge of the cube:

Volume of each cube $V=1$ cubic units (Given)

Volume of a cube =a3 where a is the edge of the cube.

$$\begin{gathered} \Rightarrow 1=a^3 \\ \Rightarrow 1^3=a^3(\sin ce{1}^3=1) \end{gathered}$$

Therefore $a=1$

Step 2: Finding volume of each rectangular prism:

The volume of each rectangular prism is the number of units cubes present in it.

There are 6 cubes in the first rectangular prism, so, volume is 6 cubic units.

The second rectangular prism has two layers of 6 cubes each so the volume is $2\times 6=12$ cubic units

Similarly third, fourth and fifth prisms have $3\times 6=18,4\times 6=24and5\times 6=30$ cubic units as volume respectively.

Step 3: Find area of the base of the prims:

All the given prisms have 6 cubes in the base layer arranged, 2 along breadth and 3 along length.

So area of the base which is a rectangle $=3\times 2=6$ square units

So the area of the base of all the prisms $=6$ square units.

Step 4: List of volumes (V) and Base areas (B)

Figure/Stack	Volume	Base Area
1	$6$	$6$
2	$12=2\times 6$	$6$
3	$18=3\times 6$	$6$
4	$24=4\times 6$	$6$
5	$30=5\times 6$	$6$

Final Answer: Hence, we can say that the volume of the given prisms is the product of their respective base areas and heights.