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?

Explanation

(i) Lateral surface area of the cubical box
`= 4 ("edge")^(2) = (4 xx 10 xx 10) cm^(2) = 400 cm^(2)`
Lateral surface area of the cuboidal box
= 2 (length + breadth) `xx` height
`= {2(12.5 + 10) xx 8} cm^(2) = (2 xx 22.5 xx 8) cm^(2) = 360 cm^(2)`
Difference in lateral surface areas
`= (400 - 360) cm^(2) = 40 cm^(2)`
Hence, the lateral surface area of the cubical box is larger than tha of the cuboidal box by `40 cm^(2)`
(ii) Total surface area of the cubical box
`= 6 ("edge")^(2) = (6 xx 10 xx 10) cm^(2) = 600 cm^(2)`
Total surface area of the cuboidal box
`= 2(lb + bh + lh)`
`= 2(12.5 xx 10 + 10 xx 8 + 12.5 xx 8) cm^(2)`
`= 2(125 + 80 + 100) cm^(2) = (2 xx 305) cm^(2) = 610 cm^(2)`
Difference in total surface area `= (610 - 600) cm^(2) = 10 cm^(2)`
Hence, the total surface area of the cubical box is smaller than of the cuboidal box by `10 cm^(2)`