Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find i) radius of the base and ii) total surface area of the cone

Solution:

Curved surface area of the cone is 308 cm² and its slant height is 14 cm.

The total surface area of the cone is the sum of the curved surface area and area of the base which is a circle.

Curved surface area of a right circular cone of base radius, r and slant height, l is πrl.

Total surface area of the cone = πrl + πr² = πr (l + r)

Let the radius be r

Slant height, l = 14 cm

Curved surface area = 308 cm²

πrl = 308

r = 308 cm²/πl

r = 308 cm²/14 cm × 7/22

= 7 cm

Total surface area = πr (l + r)

= 22/7 × 7 cm × (7 cm + 14 cm)

= 22 cm × 21 cm

= 462 cm²

Thus, radius of the cone is 7 cm and total surface area of the cone is 462 cm².

☛ Check: NCERT Solutions for Class 9 Maths Chapter 13

Video Solution:

Curved surface area of a cone is 308 cm² and its slant height is 14 cm. Find i) radius of the base and ii) total surface area of the cone

Class 9 Maths NCERT Solutions Chapter 13 Exercise 13.3 Question 3

Summary:

It is given that the curved surface area of a cone is 308 cm² and its slant height is 14 cm. We have found that radius of the cone is 7 cm and the total surface area of the cone is 462 cm².

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