Question

a cuboid 3 cm 4 cm into 5 cm is cut into unit cubes then what is the ratio of the total surface area of all the unit cubes to that of the cuboid​

Answer 1

Volume of cuboid=3*4*5=60cm^3

Volume of each cube=1cm^3

Therefore number of cubes= 60/1=60 cubes

Surface area of each cube= 6a^2=6*1^2=6

Therefore total surface area of cubes= 60*6=360sq cm

Surface area of cuboid= 2(3*4+4*5+3*5)=94 sq cm

Ratio=360:94=3.83:1

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Answer 2

Ratio of total surface area of unit cube to the cuboid=180:47

Step-by-step explanation:

Length of cuboid,l=3 cm

Breadth of cuboid=b=4cm

Height of cuboid=h=5 cm

Unit cube means the side of cube is 1  cm.

Volume of cuboid=$l\times b\times h$

By using the formula

Volume of cuboid=$3\times 4\times 5=60cm^3$

Volume of each cube=$(side)^3$

Volume of each cube=$(1)^3=1cm^3$

Number of unit cubes=$\frac{volume\;of\;cuboid}{volume\;of\; each\;cube}=\frac{60}{1}=60$

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

Total surface area of cuboid=$2(3(4)+4(5)+5(3))=2(12+20+15)=94cm^2$

Total surface area of cube=$6(side)^2$

Total surface area of each  cube=$6(1)^2=6cm^2$

Total surface area of 60 cubes=$60\times 6=360cm^2$

Ratio of total surface area of all the unit cubes to that of the cuboid=$\frac{360}{94}=\frac{180}{47}$

Ratio of total surface area of unit cube to the cuboid=180:47

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