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A cubical box has each edge10cm and another cuboidal box is 12.5cm long, 10cmwide and 8cm high (i) Which box has the greater lateral surface area and by how much? (ii) Which box has the smaller total surface area and by how much?


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Solution

Given,

Edge of a cubical box = 10cm

Length of the cuboidal box, l = 12.5cm

Breadth of the cuboidal box, b = 10cm

Height of cuboidal box, h = 8cm

(i) We know that -

The lateral surface area of a cube =4×(edge2)

So, the Lateral surface area of a cubical box =4×(edge2)

=4×(102)

=400cm2

And,

The lateral surface area of a cuboid

So, the Lateral surface area of the cuboidal box

=2(l+b)×h=2(12.5+10)×8cm2=2×22.5×8cm2=360cm2

So, the lateral surface area of the cubical box is greater than the cuboidal box by (400cm2360cm2)=40cm2.

(ii) Now,

The total surface area of a cubical box

=6×(edge)2=6×(10)2=6×100=600cm2

The total surface area of the cuboidal box is

=2(lb+bh+lh)=2×(12.5×10+10×8+8×12.5)=2×(125+80+100)=2×305=610cm2

Therefore, the total surface area of the cuboidal box is greater than the cubical box by (610cm2600cm2)=10cm2.


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