Question

Solid metal cube of side 3 inches is placed in a rectangular tank whose length, width and height are 3, 4 and 5 inches respectively. What is the volume, in cubic units, of water that the tank can now hold?
A) 20
B) 27
C) 33
D) 48

Answer 1

Hint: This is a mensuration question. To solve the above question, first we will obtain the volume of the cube and then the volume of the rectangular water tank from the given data. Then subtracting the volume of the cube from the volume of the water tank we will get the volume of water that the water tank can hold.

Complete step-by-step answer:
According to the question,
Length of the side of the solid metal cube, $ a = 3 $ inches
 $ \therefore $ The volume of the solid metal cube is, $ {a^3} = {3^3} = 27 $ cubic inches
Again it is given in the question that,
The length of the rectangular tank, $ l = 3 $
The width of the rectangular tank, $ b = 4 $
The height of the rectangular tank, $ h = 5 $
 $ \therefore $ The volume of the rectangular tank is, $ lbh = 3 \times 4 \times 5 = 60 $ cubic inches
It is given in the question that the solid metal cube is placed inside the tank.
 $ \therefore $ The volume of the water that the water tank can hold = volume of the water tank – volume of the solid metal cube
Putting the value of volume of solid metal cube and the value of volume of the tank in the above equation we get,
The volume of the water that the water tank can hold $ = 60 - 27 = 33 $ cubic units
 $ \therefore $ The volume of the water that the water tank can now hold is 33 cubic units.

Option C is correct.

Note: A cube is a three dimensional solid object bounded by six square faces. It has 6 faces, 8 vertices and 12 edges.
The volume of the cube is given by $ {a^3} $ , where a is the side of the cube.
The volume of the rectangle having length, width and height is $ lbh $ , where l is length, b is width and h is height of the rectangle.