A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.

Solution:

When the given sheet is rotated, it forms a cylinder of height/length of 25 cm. The radius of the cylinder will be 7cm.

Hence we can write:

Volume of the cylinder = πr²h

r = 7

h = 25

Volume = πr²h = (22/7) × (7) × (7) × 25 = 3850 cm³

Surface Area = 2πrh = 2 × (22/7) × 7 × 25 = 1100 cm²

✦ Try This: A rectangular sheet of dimensions 30 cm × 14 cm is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.

When the given sheet is rolled, it forms a cylinder of height/length of 25 cm. The radius of the cylinder will be 7cm.

Hence we can write:

Volume of the cylinder = πr²h

r = 14

h = 30

Volume = πr²h = (22/7) × (14) × (14) × 30 = 18,480 cm³

Surface Area = 2πrh = 2 × (22/7) × 14 × 30 = 2640 cm²

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 112

A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side. Find the volume and the whole surface area of the solid thus generated.

Summary:

A rectangular sheet of dimensions 25 cm × 7 cm is rotated about its longer side. The volume generated will be 3850 cm³ and the whole surface area of the solid generated will be 1100 cm²

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