Question

A cubical box has each edge 10cm and a cuboidal box is 10cm wide,12.5cm long and 8cm

high.

(i) Which box has the greater lateral surface area and how much?

(ii) Which box has the smaller total surface area and how much?​

Answer 1

Answer:

the cubical box is greater in part a and smaller in part b

Step-by-step explanation:

1) LSA of cube =

$4a ^{2}$

=4(10)^2

=4(100)

=400cm^2

LSA of cuboid=2(l+b) h

=2(12.5+10)8

=2(22.5)8

=45×8

=360cm^2

therefore the cubical box has greater LSA by 40cm^2

2)TSA of cube =6a^2

=6(10)^2

=6(100)

=600cm^2

TSA of cuboid=2(lb+bh+hl)

=2(12.5×10+10×8+8×12.5)

=2(125+80+100)

=2(305)

=610cm^2

therefore the cubical box had the smaller TSA by 10cm^2