Question

the length and breath and height of the cuboid are in ratio 7 :6 :5. if the surface area of cuboid is 1926 cm square find the volume of the cuboid​

Answer 1

Answer:

volume of cuboid = l×b×h

Step-by-step explanation:

1. l = 7 cm
2. b = 6 cm
3. h = 5 cm
4. l×b×h
5. 7×6×5
6. = 2100 cm

Answer 2

AnswEr :

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

The Length and breadth and height of the cuboid are in ratio 7:6:5.If the surface area of cuboid is 1926 cm².

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

The volume of the cuboid.

$\bf{\large{\underline{\rm{\blue{Explanation\::}}}}}$

Let the ratio be r

$\bf{\orange{We\:have}\begin{cases}\sf{Length\:(L)=7r}\\ \sf{Breadth\:(b)=6r}\\ \sf{Height\:(H)=5r}\\ \sf{Ar.\:of\:cuboid\:=\:1926\:cm^{2} }\end{cases}}$

$\bf{\Large{{\underline{\underline{\tt{\red{A.T.Q\::}}}}}}}$

Formula use :

$\bf{\large{\boxed{\sf{Surface\:area\:of\:cuboid\:=\:2(LB+BH+LH)}}}}}$

$\longrightarrow\tt{2(LB+BH+LH)=1926\:cm^{2} }\\\\\\\\\longrightarrow\tt{2\big[(7r*6r)+(6r*5r)+(7r*5r)\big]=1926\:cm^{2} }\\\\\\\\\longrightarrow\tt{2(42r^{2} +30r^{2} +35r^{2} )=1926cm^{2} }\\\\\\\\\longrightarrow\tt{2(107R^{2} )=1926\:cm^{2} }\\\\\\\\\longrightarrow\tt{214r^{2} \:=\:1926\:cm^{2} }\\\\\\\\\longrightarrow\tt{r^{2} \:=\:\cancel{\dfrac{1926\:cm^{2} }{214} }}\\\\\\\\\longrightarrow\tt{r^{2} \:=\:9\:cm^{2} }\\\\\\\\\longrightarrow\tt{r \:=\:\sqrt{9} cm^{2} }$

$\longrightarrow\tt{\red{r\:=\:3\:cm}}$

$\bullet\bf{\underline{Length\:(L)\::}}}$

$\leadsto\sf{7(3)\:cm}$

$\leadsto\sf{\green{21\:cm}}$

$\bullet\bf{\underline{Breadth\:(B)\::}}}$

$\leadsto\sf{6(3)\:cm}$

$\leadsto\sf{\green{18\:cm}}$

$\bullet\bf{\underline{Height\:(H)\::}}}$

$\leadsto\sf{5(3)\:cm}$

$\leadsto\sf{\green{15\:cm}}$

Now,

Formula use :

$\bf{\large{\boxed{\sf{Volume\:of\:cuboid\:=\:LBH}}}}}$

$\mapsto\tt{Volume\:=\:(21*18*15)\:cm^{3} }\\\\\\\mapsto\tt{\red{Volume\:=\:5670\:cm^{3} }}$

∴ The volume of the cuboid is 5670 cm³.