Question

A cuboid 72 cm in length, 24 cm in breadth and 64 cm in height. It is melted and recast into a single cube.
Find the edge of the cube.
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Answer 1

Answer:

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Step-by-step explanation:

Here, l = 12 cm, b = 8 cm, h = 4.5 cm

Volume of the cuboid = l×b×h

                                 =(12×8×4.5) cm3= 432 cm3

Total Surface area = 2(lb + lh+ bh)

                             =2(12×8 + 12×4.5 +8×4.5) cm2=2(96 +54 + 36) cm2=2× 186  cm2=372  cm 2

Lateral surface area = 2(l+b)×h

                             =[2(12+8)×4.5] cm2=[2(20)×4.5]  cm2=40×4.5  cm2=180 cm2

(ii)

Here, l = 26 m; b = 14 m; h =6.5 m

Volume of the cuboid =  l×b×h

                               =(26×14×6.5)m3=2366 m3

Total surface area = 2(lb + lh+ bh)

                            =2(26×14+26×6.5+6.5×14) m2=2(364+169+91) m2=2×624 m2=1248 m2

Lateral surface area = 2(l+b)×h  

                             =[2(26+14)×6.5] m2=[2×40×6.5] m2=520 m2

(iii)

Here, l = 15 m; b = 6 m; h = 5 dm = 0.5 m

Volume of the cuboid =  l×b×h

                               =(15×6×0.5) m3=45 m3

Total surface area = 2(lb + lh+ bh)  

                         =2(15×6+15×0.5+6×0.5) m2=2(90+7.5 +3) m2=2×100.5 m2= 201m2

Lateral surface area = 2(l+b)×h  

                              =[2(15+6)×0.5] m2=[2×21×0.5] m2=21 m2

(iv)

Here, l = 24 m; b = 25 cm = 0.25 m; h =6 m

Volume of the cuboid =  l×b×h  

                               =(24×0.25×6) m3=36 m3

Total Surface area = 2(lb + lh+ bh)

                           =2(24×0.25 +24×6 +0.25×6) m2=2(6+144 + 1.5) m2=2×151.5 m2=303 m2

Lateral surface area = 2(l+b)×h  

                            =[2(24+0.25)×6] m2=[2×24.25×6] m2=291 m2