Question

A rectangular container, whose base is a square of side $12$ cm, contains sufficient water to submerge a rectangular solid $8$ cm $\times$ $6$ cm $\times$ $3$ cm. Find the rise in level of the water in the container when the solid is in it.

• A. $1$ cm
• B. $2$ cm
• C. $3$ cm
• D. $4$ cm

Answer 1

The correct option is A $1$ cm

$l=12,b=12$ for container.

height of water =side of solid$=3$

total volume occupied =volume of solid +volume of water

so $lbh=lbh\left(ofsolid\right)+volofwater$

$12\times 12\times 3=8\times 6\times 3+vol.ofwater$

vol. of water$=3\times 6(2\times 12-8)$

Incontainer

Vol of water (when cube is not inserted)$=lbh$

$3\times 6(2\times 12-8)$$=12\times 12\times h$

$h=2$

so increase in water level $=3-2=1$