The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find
(i) height of the cone  (ii) slant height of the cone
(iii) curved surface area of the cone

Solution:

Volume of a cone having radius 'r', and height 'h' = 1/3πr²h 

Curved surface area of the cone having radius, 'r' and slant height, 'l' = πrl  

Slant height of the cone, l = √r² + h²  ---  Equation(3)

Diameter of the cone, d = 28 cm

Radius of the cone, r = 28/2 cm = 14 cm

i) Height of the cone, h = ?

Volume of the cone = 9856 cm³  and radius(r) = 14 cm  

1/3πr²h = 9856 cm³

h = 9856 cm³ × 3/πr²

= 9856 cm³ × 3/(14 cm × 14 cm) × 7/22

= 48 cm

ii) Slant height of the cone, l'= ?

radius(r) = 14 cm and height(h) = 48 cm 

l = √r² + h²

= √(14)² + (48)²

= √196 + 2304

= √2500

= 50 cm

iii) Curved surface area of the cone = ?

radius(r) = 14 cm and slant height(l) = 50 cm 

Curved surface area = πrl

= 22/7 × 14 cm × 50 cm

= 2200 cm²

☛ Check: NCERT Solutions Class 9 Maths Chapter 13

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Video Solution:

The volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, find (i) height of the cone (ii) slant height of the cone (iii) curved surface area of the cone

NCERT Solutions for Class 9 Maths Chapter 13 Exercise 13.7 Question 6

Summary:

It is given that the volume of a right circular cone is 9856 cm³. If the diameter of the base is 28 cm, we have found that the height of the cone is 48 cm, the slant height of the cone is 50 cm and the curved surface area of the cone is 2200 cm².

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