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. 

(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

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.