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.

Answer 2

Given,

The total surface area of a cuboid = 94 Square centimeters

Dimensions of the cuboid: Lenght = L = 3cm

Breadth = B = x cm

Height = H =4cm

To find,

I) The value of x

II) Volume of the cuboid

Solution,

We can simply solve this mathematical problem using the following process:

As per the concepts of mensuration,

The volume of a cuboid

The volume of a cuboid = Lenght x Breadth x Height

The volume of a cuboid = Lenght x Breadth x Height= LBH

Also, the total surface area of a cuboid

the total surface area of a cuboid= TSA (cuboid) = 2 x (LB + BH + LH)

=> 94 cm^2 = 2 x (3x + 4x + 12) cm^2

=> 47 = 7x + 12

=> 7x = 35

=> x = 5 cm

Now, the volume of the cuboid is:

=LBH

= 3 cm x 5 cm x 4 cm

= 60 cubic centimeters = 60 cm^3

Hence, the value of x is 5 centimeters and the volume of the cuboid is 60 cm^3.