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. (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

$\bf \LARGE \it Hey \: User!!!$

(i) given :-

→ side (edge) of the cubical box = 10cm

therefore it's lateral surface area = 4(side)²
= 4(10)²
= 4 × 100
= 400cm²

→ dimensions of the cuboidal box is 12.5cm × 10cm × 8cm.

Length = 12.5cm, breadth = 10cm and height = 8cm

therefore it's lateral surface area = 2(lh + bh)
= 2(12.5 × 8 + 10 × 8)
= 2(100 + 80)
= 2 × 180
= 360cm²

hence, lateral surface area of cubical box is greater by = 400 - 360 = 40cm²

(ii) TSA of cubical box = 6(side)²
= 6(10)²
= 6 × 100
= 600cm²

TSA of cuboidal box = 2(lb + bh + lh)
= 2(12.5 × 10 + 10 × 8 + 12.5 × 8)
= 2(125 + 80 + 100)
= 2 × 305
= 610cm²

hence, cubical box have smaller TSA by = 610 - 600 = 10cm²

$\bf \LARGE \it Cheers!!$

Answer 2

Here is your solution

Given :-

Side (edge) of the cubical box = 10cm

[1] lateral surface area = 4(side)²

=> 4(10)²

=> 4 × 100

=> 400cm²

Dimensions of the cuboidal box =12.5cm × 10cm × 8cm.

Length=12.5cm,breadth=10cm & height =8cm

=> lateral surface area = 2(lh + bh)

=> 2(12.5 × 8 + 10 × 8)

=> 2(100 + 80)

=> 2 × 180

=> 360cm²

Lateral surface area of cubical box is greater by

=> 400 - 360 = 40cm²

[ii]TSA of cubical box = 6(side)²

=> 6(10)²

=> 6 × 100

=> 600cm²

TSA of cuboidal box = 2(lb + bh + lh)

=> 2(12.5 × 10 + 10 × 8 + 12.5 × 8)

=> 2(125 + 80 + 100)

=> 2 × 305

=> 610cm²

cubical box have smaller TSA by

= 610 - 600 = 10cm²