Question

The dimensions of a cuboid are in the ratio 1:2:3 and its total surface area is 88m^s. Find the dimensions.

Answer 1

Given the question in the question tab, the following are the solution steps to answer the question.

STEP 1: Write the formula for total surface area of cuboid

`\begin{gathered} 2(lb+bh+lh) \\ \text{where l is the length} \\ b\text{ is the breadth} \\ \text{h is the height} \end{gathered}`

STEP 2: Get the dimension of the sides

`\begin{gathered} \text{ Since the dimensions of the cuboid are in the ratio 1:2:3} \\ the\text{ dimensions are given as:} \\ x,2x\text{ and }3x \\ \text{lenght}=x \\ \text{breadth}=2x \\ \text{height}=3x \end{gathered}`

STEP 3: Substitute the dimensions into the formula to get the value of x

`\begin{gathered} 2(lb+bh+lh)=88 \\ By\text{ substitution,} \\ 2((x\cdot2x)+(2x\cdot3x)+(x\cdot3x))=88 \\ \Rightarrow2(2x^2+6x^2+3x^2)=88 \\ \text{Divide both sides by 2} \\ \Rightarrow(2(2x^2+6x^2+3x^2))/(2)=(88)/(2) \\ \Rightarrow2x^2+6x^2+3x^2=44 \\ 11x^2=44 \\ \text{Divide both sides by 11} \\ (11x^2)/(11)=(44)/(11) \\ x^2=4 \\ x=\sqrt[]{4}=2 \\ x=2m \end{gathered}`

STEP 4: Get the other dimensions

`\begin{gathered} \text{breadth}=2x \\ \text{substitute 2 for x} \\ \text{breadth}=2(2)m=4m \\ \\ To\text{ get height} \\ \text{height}=3x \\ \text{substitute 2 for x} \\ \text{height}=3(2)m=6m \end{gathered}`

Hence, the dimensions are:

`2m,4m,6m`