Question

A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cmwide 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:

i) cube, 40 cm²

ii) cuboid, 10 cm²

Step-by-step explanation:

Find the lateral surface of the cube:

Lateral surface area = Perimeter x height

Lateral surface area = (4x10) x 10

Lateral surface area =  400 cm²

Find the lateral surface of the cuboid:

Lateral surface area = Perimeter x height

Lateral surface area = 2(12.5 + 10) x 8

Lateral surface area =  360 cm²

Find the difference:

Difference = 400 - 360

Difference = 40 cm²

(i) The cube has a greater lateral surface area and is greater by 40 cm²

Find the total surface area of the cube:

Total surface area of the cube = 6(10 x 10)

Total surface area of the cube = 600 cm²

Find the total surface area of the cuboid:

Total surface area of the cube = 2(12.5 x 10 + 10 x 8 + 8 x 12.5)

Total surface area of the cube =610  cm²

Find the difference:

Difference = 610 - 600

Difference = 10cm²

(ii) The cuboid has a bigger total surface area and is bigger by 10 cm²

Answer 2

$\huge \underline \mathbb {SOLUTION:-}$

From the question statement, we have

• Edge of a cube = 10 cm

• Length, l = 12.5 cm

• Breadth, b = 10cm

• Height, h = 8 cm

(i) Find the lateral surface area for both the figures

Lateral surface area of cubical box = 4 (edge)²

= 4(10)²

= 400 cm² …(1)

Lateral surface area of cubodal box = 2[lh + bh]

= [2(12.5 × 8 + 10 × 8)]

= (2 × 180) = 360

Therefore, Lateral surface area of cubodal box is 360 cm² …(2)

From (1) and (2), lateral surface area of the cubical box is more than the lateral surface area of the cubodial box. The difference between both the lateral surfaces is, 40 cm².

(Lateral surface area of cubical box - Lateral surface area of cubodial box = 400cm² - 360cm² = 40 cm² )

(ii) Find the total surface area for both the figures

The total surface area of the cubical box = 6 (edge)² = 6 (10 cm)² = 600 cm²:…(3)

Total surface area of cuboidal box

= 2[lh + bh + lb]

= [2(12.5 × 8 + 10 × 8 + 12.5 × 100]

= 610

This implies, Total surface area of cuboidal box is 610 cm² ..(4)

From (3) and (4), the total surface area of the cubical box is smaller than that of the cuboidal box. And their difference is 10cm².

Therefore, the total surface area of the cubical box is smaller than that of the cuboidal box by 10 cm².