Question

A cubical box has each edge 10cm and another cubical box is 12.5cm long, 10cm wide and 8cm high. (I) which box has the greater lateral surface area and by his much? (ii) which box Has the smaller total surface area and by how much?​

Answer 1

Answer:

(I) LSA of B is greater by 1600

Step-by-step explanation:

Given:

For Cubical box 'A'

Each Side= a= 10cm

For Cuboidal box 'B'

Length= l= 12.5cm

Breadth= b= 10cm

Height= h= 8cm

(I) Lateral surface area of 'A'= $4a^{2}$= $4(10)^{2}$= 4*100= 400cm^2

Lateral surface area of 'B'= 2h(lb)= 2*8(12.5*10)= 16*125= 2000cm^2

Hence, LSA of A< LSA of B= 400<2000

Ans. LSA of B is greater by 1600

(II) Total surface area of 'A'= $6a^{2}$= $6(10)^{2}$= 6*100= 600cm^2

Total surface area of 'B'= 2(lb+bh+lh)= 2(12.5*10 + 10*8 + 12.5*8)= 2(125+80+100)= 610cm^2

Hence, TSA of A< LSA of B= 600<610

Ans. LSA of A is smaller by 10

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