from a handpicked tutor in LIVE 1-to-1 classes

# 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 cm^{3 } and radius(r) = 14 cm

1/3πr²h = 9856 cm^{3}

h = 9856 cm^{3} × 3/πr²

= 9856 cm^{3} × 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

**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.

**☛ Related Questions:**

- Find the capacity in litres of a conical vessel with i) radius 7 cm, slant height 25 cm ii) height 12 cm, slant height 13 cm
- The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of the base. (Use π = 3.14)
- If the volume of a right circular cone of height 9 cm is 48π cm3, find the diameter of its base.
- A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?

visual curriculum