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?
(i) Lateral surface area of cubical box of edge 10cm = 4×102 cm2 = 400 cm2
Lateral surface area of cuboid box = 2(l+b)×h
= 2×(12.5+10)×8 cm2
= 2×22.5×8 cm2 = 360 cm2
Thus, lateral surface area of the cubical box is greater by (400 – 360) cm2 = 40 cm2
(ii) Total surface area of cubical box of edge 10 cm =6×102cm2=600cm2
Total surface area of cuboidal box = 2(lb + bh + lh)
= 2(12.5×10 + 10×8 + 8×12.5)cm2
= 2(125+80+100) cm2
= (2×305) cm2 = 610 cm2
Thus, total surface area of cubical box is smaller by 10 cm2
