Question

total surface area of of a cuboid with dimension 3cm into x cm into 4cm is 94 cm square find the value of x and find its volume. please explain briefly ​

Answer 1

$\underline{\underline{\sf{ \color{red}{GIVEN:-} }}}$

Total surface area of of a cuboid with dimension 3 cm × x cm × 4 cm is 94 cm².

$\underline{\underline{\sf{ \color{red}{TO\ FIND:-} }}}$

The value of x.

The volume of the cuboid.

$\underline{\underline{\sf{ \color{red}{SOLUTION:-} }}}$

◘ We know for a cuboid,

$\boxed{\bf{TSA=2(lb+lh+bh)}}$

◘ Substituting the values :-

$\sf{\longmapsto TSA=2(3\times x+x\times4+3\times4) }$

$\sf{\longmapsto 94=2(3x+4x+12)}$

$\sf{\longmapsto 94=2(7x+12)}$

$\sf{\longmapsto 94= 14x+24 }$

$\sf{\longmapsto 94-24=14x }$

$\sf{\longmapsto 70=14x }$

$\sf{\longmapsto x=\dfrac{70}{14} }$

$\bf{\longmapsto x= 5}$

∴ The value of x is 5 cm.

______________________

◘ We know for a cuboid,

$\boxed{\bf{Volume=lbh}}$

◘ Substituting the values :-

$\sf{\longmapsto Volume=3\times x \times 4}$

$\sf{\longmapsto Volume=3\times5\times4}$

$\bf{\longmapsto Volume=60\ cm^3}$

∴ The volume is 60 cm³.