Surface Area and Volume of a Right Circular Cone : Practice Problems (original) (raw)

Last Updated : 6 Feb, 2026

A right circular cone is a three-dimensional shape with one circular base and one curved surface that comes to a point called the vertex. The line joining the vertex to the centre of the base is straight and stands at a right angle to the base. It can also be formed by turning a right-angled triangle around one of its sides.

**Surface area and volume formulas for a right circular cone:

**Curved Surface Area of Right Circular Cone **πrl
**Total Surface Area of Right Circular Cone **πr(l+r)
**Volume of Right Circular Cone **1/3 × πr 2 × h

Solved Practice Problem

**1: Find the curved surface area of a cone, if its slant height is 60 cm and the radius of its base is 21 cm.

Given,

Curved Surface Area of a Cone = πrl

= π × 21 × 60

= 3.14 × 1260

= 3956.4 cm2

**2: Radius of a cone is 5 cm and vertical height is 12 cm. Find the area of the curved surface.

Given,

Curved Surface Area of a Cone = πrl

= π × 5 × 12

= 3.14 × 60

= 188.4 cm2

**3: Radius of a cone is 7 cm and area of curved surface is 176 cm 2 . Find the slant height.

Given,

Curved Surface Area of a Cone = πrl

⇒ 176 = π × 5 × l

⇒ 176 = 15.7 × l

⇒ l = 11.21cm

So, height of the cone is 11.21 cm.

**4: Find the total surface area of a right circular cone with radius 6 cm and height 8 cm.

To calculate total surface area apply the following formula

Total Surface Area = πr(l+r)

Total Surface Area = 3.14 × 6(8 + 6)

= 3.14 × 6 × 14

= 263.76 cm2

So, total surface area of the cone is 263.76 cm2.

**5: Find the total surface area of a cone, if its slant height is 21 cm and diameter of its base is 24 cm.

To calculate total surface area apply the following formula

Total Surface Area = πr(l+r)

Total Surface Area = 3.14 × 12(21 + 12)

= 3.14 × 12 × 33

= 1243.44 cm2

So, total surface area of the cone is 1243.44 cm2.

**6: Total surface area of a cone is 60π cm 2 . If the slant height of the cone be 8 cm, find the radius of the base.

So, to find the radius

60π = πr(l+r)

60 = 4r + r2

r(r-6) + 10(r-6) = 0

(r-6)(r+10) = 0

r = 6 and r = -10(not possible)

So, radius of base is 6 cm.

**7: Diameters of two cones are equal, the ratio of the slant height is 5:4, find the ratio of their curved surfaces.

Curved Surface Area of Cone = πrl

Radius of First Cone(r1) = Radius of Second Cone(r2)

Slant Height of Cone(l1):Slant Height of Cone(l2) = 5:4

Required Ratio = πr1l1/πr2l2

= 5/4

So, ratio of curved surfaces is 5/4.

**8: Find the volume of the cone, if the radius is 6cm and its height is 8cm.

Volume of Cone = 1/3 × (?r2) × h

= 1/3 × 3.14 × 6 × 6 × 8

= 401.92 cm3

So, volume of the cone is 401.92 cm3.

**9: The volume of a given cone is 100π cubic centimeters, The height of the cone is 10 cm. Find the radius of the cone.

So, to find radius of cone

Volume = 1/3 × (?r2) × h

100π = 1/3 × π × r × r × 10

r × r = 30

r = 5.4 cm

So, radius of cone is 5.4 cm.

**10: There are two cones. Cone 1 has radius of 4cm and its height is 10cm. Cone 2 has radius of 6cm and its height is 8cm. So, decide which cone has the greater volume.

To find volume of cone = 1/3 × (?r2) × h

**For Cone 1:

Volume = 1/3 × ? × 4 × 4 × 10

Volume = ?/3 × 160 cm3

**For Cone 2:

Volume = 1/3 × ? × 6 × 6 × 8

Volume = ?/3 × 288 cm3

So, cone 2 has greater volume.

Practice

Q1. Find the curved surface area of a cone, if its slant height is 48 cm and the radius of its base is 15 cm.

Q2. The radius of a cone is 8 cm and vertical height is 10 cm. Find the area of the curved surface.

Q3. The radius of a cone is 10 cm and area of curved surface is 314 cm². Find the slant height.

Q4. Find the total surface area of a right circular cone with radius 9 cm and height 12 cm.

Q5. Find the total surface area of a cone, if its slant height is 30 m and diameter of its base is 36 m.

Q6. Calculated total surface area of a cone is 90π cm². If the slant height of the cone be 10 cm, find the radius of the base.

Q7. Diameters of two cones are equal. If their slant heights are in the ratio 3:2, find the ratio of their curved surfaces.

Q8. Find the volume of the cone, if the radius is 7 cm and its height is 14 cm.

Q9. Volume of a given cone is 200π cubic centimeters. The given height of the cone is 15 cm. Find the radius of the cone.

Q10. There are two cones. Cone 1 has a radius of 6 cm and its height is 14 cm. Cone 2 has a radius of 10 cm and its height is 12 cm. Decide which cone has the greater volume.