Question

the length,breadth and hight of cuboid are in the ratio 5:4:2.if the total surface area is 1216 cm square,find the dimensions of the cuboid




​

Answer 1

Given:

• The length breadth and hight of cuboid are in the ratio 5: 4: 2.
• If the total surface area is 1216cm²

To Find:

• Dimensions of the cuboid

Solution:

Let,

• Length of cuboid = 5x
• Breadth of cuboid = 4x
• Height of cuboid = 2x

TSA of cuboid = 2(lb + bh + hl)

➠ 1216 = 2(5x × 4x) + (4x × 2x) + (2x × 5x)

➠ 1216 = 2(20x² + 8x² + 10x²)

➠ 1216 = 2 (38x²)

➠ 1216 = 76x²

➠ x² = 1216/76

➠ x² = 16

➠ x = 4cm

Now, Dimensions of cubiod

• Length of cuboid = 5x = 5 × 4 = 20cm
• Breadth of cuboid = 4x = 4 × 4 = 16cm
• Height of cuboid = 2x = 2 × 4 = 8cm

Answer 2

$\frak{Given} = \begin{cases} &\sf{The\: length\:,breadth\: and\: height\: of\: cuboid \:are\: in\: the\: ratio\: 5\::\:4\::\:2\:.} \\\\\\\\\\ &\sf{The\:total\:surface\:area\:=\:1261cm^{2}}\end{cases}$

To find:-  

• The Dimensions of the cuboid .

Assume:-

• The Length of the cuboid = 5x
• The Breadth of the cuboid = 4x
• The Heigth of the cuboid = 2x

Solution:-  

$\qquad\sf{:\implies\:Total\:Surface\:Area\:_{(Cubiod)}\:=\:2\:(lb\:+\:bh\:+\:hl\:)}$

$\qquad\sf{:\implies\:1216\:=\:2\:(5x\:\times\:4x)\:+\:(4x\:\times\:2x)\:+\:(2x\:\times\:5x)}$

$\qquad\sf{:\implies\:1216\: = \:2\:(\:20x^{2} \:+\: 8x^{2}\: +\: 10x^{2})}$

$\qquad\sf{:\implies\:1216\: = \:2\:(\:38x^{2}\:)}$

$\qquad\sf{:\implies\:1216\: = \:76x^{2}}$

$\qquad\sf{:\implies\:x^{2}\:=\:\dfrac{1216}{76}}$

$\qquad\sf{:\implies\:x^{2}\:=\:16}$

$\qquad\sf{:\implies\:x\:=\:\sqrt{16}}$

$\qquad\sf{:\implies\:x\:=\:4cm}$

Length:-

$\qquad\sf{:\implies\:Length\:_{(Cubiod)}=5x\:}$

$\qquad\sf{:\implies\:Length\:_{(Cubiod)}=5\times\:4\:}$

$\qquad\sf{:\implies\:Length\:_{(Cubiod)}=20cm\:}$

Breadth:-

$\qquad\sf{:\implies\:Breadth\:_{(Cubiod)}=\:4x\:}$

$\qquad\sf{:\implies\:Breadth\:_{(Cubiod)}=\:4\:\times\:4\:}$

$\qquad\sf{:\implies\:Breadth\:_{(Cubiod)}=\:16cm\:}$

Height:-

$\qquad\sf{:\implies\:Height\:_{(Cubiod)}=\:2x\:}$

$\qquad\sf{:\implies\:Height\:_{(Cubiod)}=\:2\:\times\:4\:}$

$\qquad\sf{:\implies\:Height\:_{(Cubiod)}=\:8cm\:}$

$\color{red}{\underline{\sf{Therefore\:the\:dimensions\:of\:the\:couboid\:are\::-}}}$

$\qquad\sf{:\implies\:Length\:_{(Cuboid)}\:=\:20cm}$

$\qquad\sf{:\implies\:Breadth\:_{(Cuboid)}\:=\:16cm}$

$\qquad\sf{:\implies\:Height\:_{(Cuboid)}\:=\:8cm}$