Question

A cubical box has edge 10cm and another cuboidal box is 12.5cm long,10cm wide and 8cm high.
1) Which box has the greater lateral surface area and byhow much?
2) Which box has the smaller total surface are and by how much?

Answer 1

Answer:

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Answer 2

Given:-

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

To find:-

1. the box has the greater lateral surface area and byhow much?
2. the box has the smaller total surface are and by how much?

Solutions:-

(i). Edge of cube = 10cm

length of box = 12.5cm

breadth of box = 10cm

height of box = 8cm

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

= 4(10)²

= 4 × 100

= 400cm²

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

= 2(12.5 × 8 + 10 × 8)

= 2(100 + 80)

= 2 × 180

= 360cm²

The lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box.

lateral surface area of cubical box - lateral surface area of cuboidal box

= 400cm² - 360cm²

= 40cm²

Hence, the lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box is 40cm²

(ii). Total surface area of cuboidal box = 2(lb + bh + lb)

= 2(12.5 × 8 + 10 × 8 + 12.5 × 10)

= 2(100 + 80 + 120)

= 2(305)

= 610cm²

The total surface area of the cubical box is smaller of the cuboidal box.

Total surface area of cuboidal box - Total surface area of cuboidal box

= 610cm² - 600cm²

= 10cm²

Hence, the total surface area of the cubical box is smaller than of the cuboidal box is 10cm².