Question

9 If the length, breadth and height of a cuboid are in the ratio 5 : 4 : 3 and its total surface area is
376 sq. m. find the dimensions of the cuboid.
12 Find the area of a tin sheet required to make a cylindrical vessel with lid if its radius of the base is
14 cm and the height is 16 cm. Find also the capacity of the vessel.
​

Answer 1

Answer:

Given length,breadth height of a cuboid are in ratio 5:4:2.

Total surface area of cuboid is 1216 sq cm.

Let length, breadth and height of cuboid be 5x, 4x and 2x respectively.

So, total surface area of cuboid =2(lb+bh+lb)

=2(5x×4x+4x×2x+5x×2x)

=2(20x

2

+8x

2

+10x

2

)

=2(38x

2

)

=76x

2

Total surface area of cuboid =1216cm

2

⇒76x

2

=1216cm

2

⇒x

2

=16

⇒x=4

Dimensions of cuboid are :

Length =5x=5×4=20 m

Breadth =4x=4×4=16 m

Height =2x=2×4=8 m

Answer 2

Answer:

10 m, 8 m, 6m

Step-by-step explanation:

Let the length, breadth and height of cuboid be 5x, 4x and 3x respectively :-

Total surface area of cuboid = 2(lb+bh+hl)

[Putting value]

376 = 2(5x*4x + 4x*3x + 3x*5x)

376/2 = (20x² + 12x² + 15x²)

188 = 47x²

x² = 4

x= √4

x=2

dimensions:-

l = 5*2=10m

b = 4*2=8m

h = 3*2=6m

Hope it helps!!

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