A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm

1.	A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 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» Each edge of cubical box, a = 10 cm. (i) Curved Surface Area = 4a² = 4(10)² = 4 × 100 = 400 cm² . Length of cuboid box, l = 12.5 cm. b = 10 cm h = 8 cm. Curved Surface area of Cuboid, A = 2h (l+ b) A = 2 × 8(12.5 + 10) = 16 × 22.5 = 360 cm² . ∴ 400 – 360 = 40 cm² . L.S.A. of cuboid box is 40 cm² greater than rectangular cuboid. (ii) Total surface area of cube (T.S.A.) = 6a² = 6(10)² = 6 × 100 = 600 cm² . T.S.A. of cuboid = 2(Ib + lh + bh) = 2[ 12.5 × 10 + 12.5 × 8 + 10 × 8] = 2 (125 + 100 + 80) = 2 × 305 = 610 cm² . Here, cuboid box’s T.S.A. is more than T.S.A. of cubical box, i.e, 610 – 600 = 10 cm² more.

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 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»

Each edge of cubical box, a = 10 cm.

(i) Curved Surface Area = 4a² = 4(10)²

= 4 × 100

= 400 cm² .

Length of cuboid box, l = 12.5 cm.

b = 10 cm h = 8 cm.

Curved Surface area of Cuboid, A = 2h (l+ b)

A = 2 × 8(12.5 + 10)

= 16 × 22.5 = 360 cm² .

∴ 400 – 360 = 40 cm² .

L.S.A. of cuboid box is 40 cm² greater than rectangular cuboid.

(ii) Total surface area of cube (T.S.A.) = 6a²

= 6(10)² = 6 × 100 = 600 cm² .

T.S.A. of cuboid = 2(Ib + lh + bh)

= 2[ 12.5 × 10 + 12.5 × 8 + 10 × 8]

= 2 (125 + 100 + 80)

= 2 × 305 = 610 cm² .

Here, cuboid box’s T.S.A. is more than T.S.A. of cubical box,

i.e, 610 – 600 = 10 cm² more.