Question

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

a) which box has the greater lateral surface area and by how much?

b) which box has the smaller total surface area and by how much?​

Answer 1

Answer:

a)

l.s.a of cube =4a²

=4×100=400cm²

l.s.a of cuboid

2h(l+b)

2×8(22.5)

45×8=360 cm²

so cube has a greater l.s.a by 40 cm²

b)t.s.a of cubical box=6a²

t.s.a=6×10²

=600cm²

t.s.a of cuboidal box = 2(lb+bh+lh)

2(125+80+100)

2(305)=610cm²

so cubical box have a smaller t.s.a by 10 cm²

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Answer 2

a, lateral surface area of cube = 4(a)²

= 4 × 10²

= 4× 100

= 400cm²

lateral surface area of cuboid = 2(l+b)×h

= 2(12.5+10)×8cm

=2×22.5×8cm

= 360 cm²

so , the lateral surface area of cube is greater than the area of cuboid

and by how much

= the area of cube - area of cuboid

= 400cm² - 360cm²

= 40cm²

b, total surface area of cube = 6(a)²

= 6×(10)²

=6×100

=600cm²

total surface area of cuboid = 2(lb+bh+hl)

= 2(12.5×10+10×8+8×12.5)

=2(125+80+100)

=2(305)

=610cm²

so, the total surface of area of cube is smaller than the area of cuboid

and by how much

= total surface area of cuboid - total surface area of cube

=610cm²-600cm²

=10cm²

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