Question

the Length breadth and height of the cuboid are the ratio 7 : 6 : 5 if the surface area of the cuboid is 1926 CM square find the volume of the cuboid

Answer 1

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

Length be 7p

Breadth be 6p

Height be 5p

$\textbf{\underline{By\;the\;Question}}$

${\boxed{\sf\:{Surface\;area\;of\;cuboid=1926\;cm^2}}}$

2(lb + bh + hl) = 1926

2(7p × 6p + 6p × 5p + 5p × 7p) = 1926

${\boxed{\sf\:{42p^2+30p^2+35p^2=\dfrac{1926}{2}}}}$

107p² = 963

${\boxed{\sf\:{p^2=\dfrac{963}{107}}}}$

p² = 9

p = √9

p = 3

Hence,

$\textbf{\underline{Length\;(l)}}$

= 7 × 3

= 21 cm.

$\textbf{\underline{Breadth\;(b)}}$

= 6 × 3

= 18 cm.

$\textbf{\underline{Height\;(h)}}$

= 5 × 3

= 15 cm.

Now,

${\boxed{\sf\:{Volume\;of\;Cuboid=l\times b\times h}}}$

= 21 × 18 × 15

= 5670 cm³