Question

Anshuman is preparing to make an ice sculpture. He has a block of ice of dimensions $3$ feet $\times$ $4$ feet $\times$$5$ feet that he wants to reduce in size by shaving off the same amount from the lengths, width, and height. He wants to reduce the volume of the ice block to $24$ cubic feet. Then the polynomial equation to model this situation is

• A. $x^3-15x^2+47x+36=0$
• B. $-x^3+47x^2-12x+38=0$
• C. $-x^3+12x^2-47x+36=0$
• D. $x^3+12x^2+47x-36=0$

Answer 1

The correct option is C

$-x^3+12x^2-47x+36=0$

Explanation for the correct option:

The volume of ice:

Given measures of ice:

Length,$l=3feet$, Width, $b=4feet$, Height, $h=5feet$ and Reduced volume$=24cubicfeet$.

Suppose, Anshuman shaves off $x$ feet each from the length, width, and height.

So, now the reduced dimensions of ice are:

Length,$l=\left(3-x\right)$, Width, $b=\left(4-x\right)$ and Height, $h=\left(5-x\right)$.

The reduced volume of ice$=\left(3-x\right)\left(4-x\right)\left(5-x\right)$

as we know that,

$(3-x)(4-x)(5-x)=24$ [ $\because$volume of cuboid $=$ length $\times$ width $\times$ height]

$$\begin{gathered} \Rightarrow \left(3-x\right)\left(4-x\right)\left(5-x\right)=24 \\ \Rightarrow (12-3x-4x+x^2)(5-x)=24 \\ \Rightarrow 60-12x-15x+3x^2-20x+4x^2+5x^2-x^3=24 \\ \Rightarrow -x^3+12x^2-47x+36=0 \end{gathered}$$

Hence, the correct option is ‘C’.