Question

If the sum of the volumes of two shapes is equal to the volume of the third shape, which of the following options is correct?
Note: Consider the volume of the unit cube used in all $3$ shapes is of volume $1$ cu m.

• A. Shape A + Shape B = Shape C
• B. Shape A + Shape C = Shape B
• C. Shape C + Shape B = Shape A
• D. Shape B + Shape A = Shape C

Answer 1

The correct option is B Shape A + Shape C = Shape B

Number of cubes in Shape A $=$ Number of unit cubes in the base layer $\times$ Number of layers $=2\times 2=4$cubes
Volume of Shape A $=4$ cu m

Number of cubes in Shape B $=$ Number of unit cubes in the base layer $\times$ Number of layers $=4\times 3=12$ cubes
Volume of Shape B $=12$ cu m

Number of cubes in Shape C $=$ Number of cubes in the base layer $\times$ Number of layers $=4\times 2=8$ cubes
Volume of Shape C $=8$ cu m

So clearly, $4$ cu m $+8$ cu m $=12$ cu m
Therefore, Shape A $+$ Shape C = Shape B
Thus, Option C is correct.