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
(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?
Answers
Given that,
Edge of cubical box is 10 cm.
Length of cuboidal box is 12.5 cm.
Breadth of cuboidal box is 10 cm.
Height of cuboidal box is 8 cm.
Lateral surface area of cube = 4 (edge)²
➝ 4 × (10)²
➝ 4 × 100
➝ 400
Lateral surface area of cubical box is 400 cm².
Lateral surface area of cuboid = 2 × height (length + breadth)
➝ 2 × 8 (12.5 + 10)
➝ 16 (12.5 + 10)
➝ 200 + 160
➝ 360
Lateral surface area of cuboidal box is 360 cm².
Total surface area of cube = 6 (edge)²
= 6 × (10)²
= 6 × 100
= 600
Total surface area of cubical box is 600 cm².
Total surface area of cuboid = 2[(length × breadth) + (breadth × height) + (length × height)]
= 2 × (12.5 × 10 + 10×8 + 8×12.5)
= 2 × (125 - 160 + 100)
= 250 + 160 + 200
= 610
Total surface area of cuboidal box is 610 cm².
_______________________________
(i) Cubical box has greater lateral surface are than cuboidal box.
➝ 400 - 360
➝ 40
Lateral surface area = 40 cm².
So,
Cubical box has greater lateral surface than cuboidal box by 40 cm²
(ii) Cubical box has smaller total surface area.
➝ 610 - 600
➝ 10
Total surface area = 10 cm².
Cubical box has smaller total surface area than cuboidal box by 10 cm².