Question

the lengh,breadth and height of a cuboid are in the ratio 7:6:5. If the surface area of a cubois is 1926cm^2,find its dimensions. also find the area of the cuboid​

Answer 1

$\large\sf\underline{Given\::}$

• Ratio of length , breadth and height is 7 : 6 : 5 .

• Surface area of a cuboid = $\sf\:1926\:cm^{2}$

‎

‎

$\large\sf\underline{To\:find\::}$

• Dimension and area of the cuboid.

‎

‎

$\large\sf\underline{Solution\::}$

Ratio of length , breadth and height is 7 : 6 : 5 .

Let's assume that :

• Length = 7x

• Breath = 6x

• Height = 5x

‎

‎

It's given that :

※ Surface area of a cuboid = $\sf\:1926\:cm^{2}$

‎

‎

We know ,

${\sf{{\pink{★\:Surface\:area\:of\:cuboid\:=\:2(lb+bh+lh)}}}}$

$\sf\implies\:2(lb+bh+lh)=1926$

• Substituting the value of l , b and h .

$\sf\implies\:2(7x \times 6x + 6x \times 5x+ 7x \times 5x)=1926$

$\sf\implies\:2(42x^{2} + 30x^{2} + 35x^{2} )=1926$

$\sf\implies\:2(107x^{2} )=1926$

$\sf\implies\:214x^{2}=1926$

$\sf\implies\:x^{2}=\cancel{\frac{1926}{214}}$

$\sf\implies\:x^{2}=9$

$\sf\implies\:x=\sqrt{9}$

$\large{\mathfrak\red{\implies\:x\:=\:3}}$

‎

‎

Therefore, Dimensions of cuboid :

• Length = 7x = 7 × 3 = ${\sf{{\purple{21\:cm}}}}$

• Breadth = 6x = 6 × 3 = ${\sf{{\purple{18\:cm}}}}$

• Height = 5x = 5 × 3 = ${\sf{{\purple{15\:cm}}}}$

‎

‎

Now let's find the area of the cuboid.

We know : Area of cuboid = Volume of cuboid

${\sf{{\pink{★\:Volume\:of\:cuboid\:=\:l \times b \times h}}}}$

• Substituting the value of l , b and h

$\sf\implies\:Volume\:=\: 21 \times 18 \times 15$

$\sf\implies\:Volume\:=\: 378 \times 15$

${\sf{{\purple{\implies\:Volume\:=\:5670\:cm^{3}}}}}$

‎

‎

!! Hope it helps !!