Total surface area of a cuboid is 148 cm square and length and breadth

1.	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» 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$}\put(11.1,5.8){$<klux>B</klux>$}\put(11.08,8.9){$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)

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»

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$}\put(11.1,5.8){$<klux>B</klux>$}\put(11.08,8.9){$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)