Question

Question 5
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

Edge of cube = 10 cm
Length (l) of box = 12.5 cm
Breadth (b) of box = 10 cm
Height (h) of box = 8 cm
Lateral surface area of cubical box = 4 $(edge{)}^2$
$=4(10cm{)}^2$
$=400c{m}^2$
Lateral surface area of cubodial box = 2[lh + bh]
$=\left[2\right(12.5\times 8+10\times 8\left)\right]c{m}^2$
$=(2\times 180)c{m}^2$
$=360c{m}^2$
Clearly, the lateral surface area of the cubical box is greater than the lateral surface area of the cubodial box.
Lateral surface area of cubical box – Lateral surface area of cubodial box $=400c{m}^2-360c{m}^2=40c{m}^2$
Total surface area of the cubical box $=6(edge{)}^2=6(10cm{)}^2=600c{m}^2$
Total surface area of cuboidal box
$=2[lh+bh+lb]=2[12.5\times 8+10\times 8+12.5\times 100]c{m}^2$
$=610c{m}^2$
Clearly, the total surface area of the cubical box is smaller than that of the cuboidal box.
Total surface area of cuboidal box - Total surface area of cubical box $=610c{m}^2–600c{m}^2=10c{m}^2$
Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by $10c{m}^2$.