Question

A cubical box has each edge 10 cm and another cuboidal box is 19.5cm long, 15 cm wide and 11 cm 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?​

Answer 1

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Sol. Volume of each cube = 64 cm3

∴ Total volume of the two cubes = 2 × 64 cm3

= 128 cm3

Let the edge of each cube = x

∴ x3 = 64 = 43

∴ x = 4 cm

Now, Length of the resulting cuboid l = 2x cm

Breadth of the resulting cuboid b = x cm

Height of the resulting cuboid h = x cm

∴ Surface area of the cuboid = 2 (lb + bh + hl) = 2[(2x . x) + (x . x) + (x . 2x)]

= 2[(2 × 4 × 4) + (4 × 4) + (4 × 2 × 4)] cm2

= 2 [32 + 16 + 32] cm2 = 2[80] cm2 = 160 cm2.

Answer 2

Explanation:

(i) Lateral surface area of cube = 4edge

2

=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)cm

2

(ii) Total surface area of cube = 6edge

2

=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) cm

2