Question

Total surface area of a cuboid is 148 cm square and length and breadth as respectively 4 cm and 6 cm find the height

Answer 1

AnswEr:-

Height of cuboid = 5 cm

$\rule{200}{2}$

⋆ DIAGRAM OF CUBOID:-

$\setlength{\unitlength}{0.5 cm}\begin{picture}(12,4)\thicklines\put(1,4){ . }\put(5.5,5.5){ A }\put(11.1,5.8){ B }\put(11.08,8.9){ C }\put(5.35,8.5){ D }\put(3.45,10.15){ E }\put(3.4,7.15){ F }\put(9.14,10.235){ H }\put(9.14,7.3){ G }\put(3.3,6.3){ 4\:cm }\put(7.75,6.2){ 6\:cm }\put(11.1,7.5){ 5\:cm }\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

Given conditions:-

↠ TSA of cuboid = 148 cm²

↠ Length(l) = 4 cm

↠ Breadth (b) = 6 cm

To find out:-

↠ Height of cuboid = ?

Solution:-

Here, length & breadth has been given.

As we know formula:-

☛ $\boxed{\boxed{\tt{\blue{TSA \: of \: cuboid = 2(lb + bh + hl) }}}}$

• Putting values:-

⇒ 148 = 2 [(4 × 6) + (6 × h) + (h × 4)]

⇒ 148 = 2[24 + 6h + 4h]

⇒ 24 + 10h = 148/2

⇒ 24 + 10h = 74

⇒ 10h = 74 - 24

⇒ 10h = 50

⇒ h = 50/10

⇒ h = 5

So, height of cuboid = 5 cm.

Additional information:-

⇒ Volume of cuboid = lbh

⇒ Surface area of cuboid = 2(l + b) × h

⇒ Diagonal of cuboid = √(l² + b² + h²)

Answer 2

Given :

• Total surface area of a cuboid is 148 cm².

• Length of the cuboid = 4 cm.

• Breadth of the cuboid = 6 cm.

To find :

• Height of the cuboid = ?

Step-by-step explanation:

Total surface area of a cuboid is 148 cm². [Given]

We know that,

Total Surface Area of cuboid =2(lb+bh+hl)

Substituting the values in the above formula, we get,

➮ 148 = 2 ( 4 × 6 + 6 × h + h × 4)

➮ 148 = 2 ( 24 + 6h + 4h )

➮ 148 = 2 ( 24 + 10h)

➮ 148 = 48 + 20h

Or, 20h + 48 = 148

➮ 20h = 148 - 48

➮ 20h = 100

h = 100 / 20

h = 5

Hence, The height of the cuboid = 5 cm.