Question

36. 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

Answer:

Edge of cube= a = 10cm

length (l) of box = 12.5cn

breadth (b) of box = 10cm

height (h) of box = 8cm

lateral surface area of cubical box =4(a)square

= 4(10)square

=4 x (100)

= 400cm square

lateral surface area of cuboidal box =2(lh+bh)

=(2(12.2 x 8 + 10 x 8))cm square

=(2(100 + 80)) cm square

= (2 x 180) cm square

=360 cm square

ii

total surface area of cubical box =6(a) square

= 6(10) square

= 6 x (100)

= 600 cm square

total surface area of cuboidal box =2(lh+ bh+lb)

= 2(12.5 x 8 +10 x 8 +12.5 x 10) cm square

= 2(100 + 80 + 125) cm square

= (2 x 305) cm square

= 610 cm square

so,

total surface area of cubical box < total surface area of cuboidal box

total surface area of cubical box - total surface area of cuboidal box

= 610 cm square - 600 cm square

= 10 cm square

therefore,

total surface area of cubical box is smaller than the total surface area of cuboidal box by 10 cm square