Question

plzzzzzz help me...... ​

Answer 1

${ \bold { \underline{\large\purple{Correct \: Question : - }}}} \:$

The length, breadth and height of a cuboid(wooden plank) are in the ratio 6:5:3. If the total surface area is 504 cm², find its dimension.

${ \bold { \underline{\large\pink{Given : - }}}} \:$

★ Area of the Cuboid ( Wooden plank )

★ Ratio of l : b : h = 6 : 5 : 3

${ \bold { \underline{\large\pink{Find: - }}}} \:$

★ Dimensions of the plank.

${ \bold { \underline{\large\purple{Diagram : - }}}} \:$

$\setlength{\unitlength}{0.74 cm}\begin{picture}\thicklines\put(5.6,5.4){\bf A}\put(11.1,5.4){\bf B}\put(11.2,9){\bf C}\put(5.3,8.6){\bf D}\put(3.3,10.2){\bf E}\put(3.3,7){\bf F}\put(9.25,10.35){\bf H}\put(9.35,7.35){\bf G}\put(3.5,6.1){\sf 10\:cm}\put(7.7,6.3){\sf 12\:cm}\put(11.3,7.45){\sf 6\:cm}\put(6,6){\line(1,0){5}}\put(6,9){\line(1,0){5}}\put(11,9){\line(0,-1){3}}\put(6,6){\line(0,1){3}}\put(4,7.3){\line(1,0){5}}\put(4,10.3){\line(1,0){5}}\put(9,10.3){\line(0,-1){3}}\put(4,7.3){\line(0,1){3}}\put(6,6){\line(-3,2){2}}\put(6,9){\line(-3,2){2}}\put(11,9){\line(-3,2){2}}\put(11,6){\line(-3,2){2}}\end{picture}$

${ \bold { \underline{\large\purple{Solution : - }}}} \:$

So , Firstly consider length , breadth and height of a cuboid respectively ,

l = 6 x cm ,

b = 5 x cm ,

h = 3 x cm

Now,

As we know the Formula of T.SA of cuboid

Then,

Total Surface Area of the cuboid = 504cm²

↬ 2( lb + bh + lh ) = 504

↬ 2[ 6x × 5x + 5x × 3x + 6x × 3x ] = 504

↬ 2( 30x² + 15x² + 18x² ) = 504

↬ 2 × 63x² = 504

↬ x² = 504 /( 2 × 63 )

$\longmapsto\tt{x^2=\cancel\dfrac{504}{126}}$

↬ x² = 4

↬ x = √4

↬ x = 2

Hence, Now

l = 6x

= 6 × 2

= 12 cm

b = 5x

= 5 × 2

= 10 cm

h = 3x

= 3 × 2

= 6 cm

Note :-

➤ Kindly see the diagram from site. (brainly.in)

━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

Answer:

Let length of the cuboid = 6x

Breadth of the cuboid = 5x

Height of the cuboid = 3x

Total surface area of the given cuboid = 2 (I x b + b x h + h x l)

= 2(6x x 5x + 5x x 3x + 3x x 6x) = 2(30×2 + 15×2 + 18×2)

= 2 x 63×2 = 126x²

But we are given total surface area of the given cuboid = 504 cm²

126x² = 504 cm²

=> x² = 504/126

=> x² = 4

=> x = √4

=> x = 2 cm.

Length of the cuboid = 6x = 6 x 2 = 12 cm

Breadth of the cuboid = 5x = 5 x 2 = 10cm

Height of the cuboid = 3x = 3 x 2 = 6 cm

Volume of the cuboid = l x b x h = 12 x 10 x 6 = 720 cm³

hope this helps you