Question 5 - Area Of Cube/ Cuboid - Chapter 11 Class 9 Surface Areas and Volumes

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Question 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 Question 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. Question 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.