NCERT Solutions for Class 9 Maths Chapter 13

Important NCERT Questions

Surface Areas and Volumes

NCERT Books for Session 2022-2023

CBSE Board, UP Board and Other state Boards

EXERCISE 13.1

Page No:213

Questions No:5

(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?

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(i) Side of cubical box l = 10 cm

Curved surface area of cubical box = 4l² = 4(10)² cm² = 4(100) cm² = 400 cm²

Length of cuboidal box l = 12.5 cm, breadth b = 10 cm and height h = 8 cm

Curved surface area of cuboidal box = 2(l + b)h = 2(12.5 + 10) × 8 cm² = 2(22.5) × 8 cm² =360 cm²

Difference between surface area of two boxes = 400 cm² – 360 cm² = 40cm²

Hence, the curved surface area of cubical box is more than cuboidal box by 40 cm².

(ii) Side of cubical box l = 10 cm

Total surface area of cubical box = 6l² = 6(10)² cm² = 6(100) cm² = 600 cm²

Length of cuboidal box l = 12.5 cm, breadth b = 10 cm and height h = 8 cm

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

= 2(12.5 × 10 + 10 × 8 + 8 × 12.5) cm² = 2(125 + 80 + 100) cm²

= 2(305) cm²

= 610 cm²

Difference between total surface areas of two boxes = 610 cm² – 600 cm² = 10 cm²

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