Question

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm
wide and 8 cm high.
(1) 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?​

Answer 1

(i) Lateral surface area of cube = 4edge2

=4(10)2=400

lateral surface area of cuboid =2h(l+b)

2×8(12.5+10)=16×22.5=360

So, the lateral surface area of the cube is larger by (400−360=40)cm2

(ii) Total surface area of cube = 6edge2

=6(10)2=600

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

2(12.5×10+10×8+8×12.5)=2(125+80+100)=610

So, the total surface area of cuboid is larger by (610−600=10) cm2

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