Question

How many $1cm \times 1cm \times 1cm$ blocks are needed to build the rectangular prism shown ?

(A) 10
(B) 12
(C) 33
(D) 36

Answer 1

Hint: In this particular type of question we need to first find the volume of the small blocks and then the volume rectangular prism (cuboid) using its sides. In order to find the number of blocks to build the rectangular prism we need to divide the volume of the prism with the volume of a small block.

Complete step-by-step answer:
Volume of a small block = $1cm \times 1cm \times 1cm = 1c{m^3}$ ( since volume =$sid{e^3}$ )
To get the volume of a rectangular prism, we multiply the length of the prism by the width of the prism by the height of the prism.
Volume of the rectangular prism = $4 \times 3 \times 3 = 36c{m^3}$
Number of blocks required = $\dfrac{{Volume{\text{ }}of{\text{ }}the{\text{ }}rectangular{\text{ }}prism}}{{Volume{\text{ }}of{\text{ }}a{\text{ }}small{\text{ }}block}}$
$ \Rightarrow Number{\text{ }}of{\text{ }}blocks{\text{ }}required = \dfrac{{36c{m^3}}}{{1c{m^3}}} = 36$

Note: We need to recall the formula for volume of a cuboid to solve such questions. Remember to change the dimensions in questions where the dimensions of both solids are different, also the final quantity we get should be dimensionless.