Question

Anshuman is preparing to make an ice sculpture. He has a block of ice as shown in the below figure that he wants to reduce in size by shaving off the same amount from the length, width and height. He wants to reduce the volume of the ice block to 24 cubic feet. How much should he shave from each side so that the volume of the block will reduce to 24 cubic feet?

Answer 1

Hint: Let us assume that Anshuman has shaved x ft. from each side of the ice cube so the subtract x from the length, width and height given of the ice cube. And then multiply the reduced length, width and height to each other and equate it to 24 cubic feet. Now, solve this cubic equation and get the value of x. The value of x is the shaved amount from each side.

Complete step-by-step answer:
The figure given in the above problem has length, width and height as 3 ft., 5 ft and 4 ft respectively.

Anshuman wants to make an ice sculpture by shaving off the equal amount of each side so let us assume that Anshuman has shaved x ft. from each side of the given cube then length, width and height are reduced by x ft.
Subtracting x ft. from length, width and height we get,
Length $=\left( 3-x \right)ft.$
Width $=\left( 5-x \right)ft.$
Height $=\left( 4-x \right)ft.$
Now, to get the volume of the reduced cube we have to multiply the above length, breadth and height so multiplying the reduced length, width and height we get,
$\left( 3-x \right)\left( 5-x \right)\left( 4-x \right)$
And it is given that reduced volume of the cube is 24 cubic metre so equating the above multiplication to 24.
$\left( 3-x \right)\left( 5-x \right)\left( 4-x \right)=24$………… Eq. (1)
By hit and trial we can find the solution of x so put $x=1$ in the above solution we get,
$\begin{align}
  & \left( 3-1 \right)\left( 5-1 \right)\left( 4-1 \right)=24 \\
 & \Rightarrow 2\left( 4 \right)\left( 3 \right)=24 \\
 & \Rightarrow 24=24 \\
\end{align}$
As you can see that putting $x=1$ in eq. (1), L.H.S and R.H.S are coming as equal so $x=1$ is satisfying the eq. (1).
Hence, the value of x is 1.
As we have assumed that x is the shaved off amount so Anshuman has shaved off 1 ft. to get the reduced cube.


Note: An interesting point to be noted here is that the dimensions (length, width and height) of the ice cube are all unequal which is representing a cuboid. We usually think that the word “ice cube” contains the word cube which means all the sides are equal but here the dimensions of the ice cube are unequal. Isn’t it contradicting?
The answer is if you practically look at an ice cube, the cubes of the tray in which ice is made is not perfectly in the shape of a cube so the ice cube in the question also is not perfectly in the shape of a cube with all the dimensions equal.