Ex 13.1, 5 (Introduction)
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
Which box has the greater lateral surface area and by how much?
Lateral Surface Area of cube
Lateral Surface area of cube = Area of 4 faces
= 4 × (Side)2
= 4a2
Lateral Surface Area of cuboid
Lateral surface area of cuboid
= surface Area of cuboid – Area of top – Area of bottom
= 2(lb + bh + lh) – lb – lb
= 2(lb) + 2(bh) + 2(lh) – 2(lb)
= 2lh + 2bh
Ex 13.1, 5
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
Which box has the greater lateral surface area and by how much?
Edge of cube = a = 10 cm
Length (l) of box = 12.5 cm
Breadth (b) of box = 10 cm
Height (h) of box = 8 cm
Lateral surface area
of cubical box = 4(a)2
= 4(10)2
= 4 × (100)
= 400 cm2
So,
Lateral surface area of cubical box > Lateral surface area of cuboidal box
Lateral surface area of cubical box − Lateral surface area of cuboidal box
= 400 cm2 − 360 cm2
= 40 cm2
Therefore, the lateral surface area of the cubical box is greater than the lateral surface area of the cuboidal box by 40 cm2.
Ex 13.1, 5
A cubical box has each edge 10 cm and another cuboidal box is 12.5 cm long, 10 cm wide and 8 cm high.
(ii) Which box has the smaller total surface area and by how much?
Edge of cube = a = 10 cm
Length (l) of box = 12.5 cm
Breadth (b) of box = 10 cm
Height (h) of box = 8 cm
So,
Total surface area of cubical box < Total surface area of cuboidal box
Total surface area of cuboidal box − Total surface area of cubical box
= 710 cm2 − 600 cm2
= 110 cm2
Therefore,
total surface area of the cubical box is smaller than the total surface area of the cuboidal box by 110 cm2.

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.