A cubical box has each edge 10cm and another cuboidal box is 12.5cm long, 10cm wide and 8cm high.Which box has the greater lateral surface area and by how much?
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Solution
(i) Lateral surface area of cube
=4 (edge)2
=4(10)2=400 cm2
Lateral surface area of cuboidal box
=2(lh+bh) =2(12.5×8+10×8)
=2×180=360 cm2
∴ Lateral surface area of cubical box > Lateral surface area of cuboidal box ⇒ Difference: 400−360 cm2 =40 cm2
(ii) Total surface area of cubical box
=6(edge)2 =(6)2=300 cm2
Total surface area of cuboidal box
=2(lb+bh+lh) =2(12.5×100+10×8+12.5×8) =610 cm2
Total S.A of cuboidal box < cuboidal total S.A Difference =610−600cm2=10 cm2