Question

There are 2 cubes A and B each of volume $Xc{m}^3$. Cube B is cut into smaller cubes each of volume $Yc{m}^3$. The surface area and volumes of the resulting cubes are compared

Statement (S1): The ratio of volumes of A and B(after cutting) = 1:1

Statement (S2): The ratio of surface areas of A and B(after cutting) = 1:1

• A. S1 is true but S2 is false
• B. S1 is false but S2 is true
• C. S1 and S2 are true
• D. S1 and S2 are false

Answer 1

The correct option is A

S1 is true but S2 is false

Volume is the space occupied by a body. So cutting an object does not change its volume. Therefore cube A and cube B after cutting will have the same volume.

The surface area of a body depends on the number of surfaces. So cutting a body creates new surfaces. Hence surface area of the newly formed cubes would be greater than that of cube A.

Let us try to understand this with an example.

Assume $X=64c{m}^3$ and $Y=1c{m}^3$.

$\therefore$ Number of cubes $=\frac{64}{1}=64$

Volume of cube A $=64c{m}^3$

Volume of cube B after cutting $=64\times 1=64c{m}^3$

Hence, their volumes are the same.

Length of side of cube A $=\sqrt[3]{364}=4cm$

Surface area of cube A $=6\times 4^2=96c{m}^2$

Length of cube B after cutting $=1cm$

Surface area of 1 cube $=6\times 1^2=6c{m}^2$

Surface area of 64 such cubes $=64\times 6=384c{m}^2$

Hence their surface areas are not the same.

$\therefore$ S1 is true and S2 is false