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# Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, find its curved surface area.

**Solution:**

The Curved surface area of a cylinder of height h and radius r = 2πrh

The area of the bases of the cylinder is = 2πr²

It is Given that

4(2πrh) = 6(2πr²)

8h = 12r

h = 12 cm

Therefore

r = (8 × 12)/12 = 8 cm

The curved surface area of the cylinder = 2 × (22/7) × 8 × 12 = 603.43cm²

**✦ Try This:** Seven times the area of the curved surface of a cylinder is equal to 8 times the sum of the areas of its bases. If its height is 8 cm, find its curved surface area.

The Curved surface area of a cylinder of height h and radius r = 2πrh

The area of the bases of the cylinder is = 2πr²

It is Given that

7(2πrh) = 8(2πr²)

7h = 8r

r = 7h/8

h = 8 cm

Therefore

r = (7 × 8)/8 = 7 cm

The curved surface area of the cylinder = 2 × (22/7) × 7 × 8 = 352cm²

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

**NCERT Exemplar Class 8 Maths Chapter 11 Problem 114**

## Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, find its curved surface area.

**Summary:**

Four times the area of the curved surface of a cylinder is equal to 6 times the sum

of the areas of its bases. If its height is 12 cm, The curved surface area is 603.43cm²

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