# Volume of a right circular cone

## Trending Questions

**Q.**Question 3

The height of a cone is 15 cm. If its volume is 1570 cm3, find the radius of its base.

[Use π=3.14]

**Q.**

Choose the correct answer in each of the following :

If the height of a cone is doubled then its volume is increased by

(a) 100% (b) 200% (c) 300% (d) 400%

**Q.**

Question 8

Two solid cones A and B are placed in a cylindrical tube. The ratio of their capacities are 2:1. Find the heights and capacities of cones. Also, find the volume of the remaining portion of the cylinder.

**Q.**

The radius and the height of a right circular cone are in the ratio 5:12.If its volume is 314 cubic metre, find the slant height and radius (Use π=3.14)

**Q.**A right angled triangle of sides 3 cm, 4 cm and 5 cm is rotated about the side 3 cm then, the volume of the cone formed is

- 16π cm2
- 9π cm2
- 12π cm2
- 8π cm2

**Q.**

If the volume of a right circular cone of height 9 cm is 48 π cm3, find the diameter of its base.

**Q.**

Find the volume of the largest right circular cone that can be fitted in a cube whose edge is 14 cm.

**Q.**Question 3 (ii)

A cloth having an area of 165 m2 is shaped into the form of a conical tent of radius 5 m.

(i) Find the volume of the cone.

**Q.**

The radius and the height of a right circular cone are in the ratio 5:12.If its volume is 2512 cubic cm, find the slant height and radius (Use π=3.14)

**Q.**

Find the volume of a right circular cone with:

(i) radius 6 cm, height 7 cm

(ii) radius 3.5 cm, height 12 cm

(iii) height 21 cm and slant height 28 cm

**Q.**There are 25 persons in a tent which is conical in shape. Every person needs an area of 4 sq.m. of the ground inside the tent. If height of the tent is 18 m, find the volume of the tent.

**Q.**

Two cones have their heights in the ratio 1 : 3 and the radii of their bases in the ratio 3:1.Show that their volumes are in the ratio 3 : 1.

**Q.**

The radius of the base of a cone is $14cm$ and its height is $24cm$. Find the volume, curved surface area and total surface area of the cone.

**Q.**Question 2

A semi-perimeter sheet of metal of diameter 28 cm is bent to form an open conical cup. Find the capacity of the cup.

**Q.**

Finds 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.

**Q.**

Find the weight of a solid cone whose base is of diameter 14 cm and vertical height 51 cm, supposing the material of which it is made weighs 10 grams per cubic cm.

**Q.**

The circumference of the base of a cone is 44 cm and its slant height is 25 cm. Find the volume of the cone.

- 1232 cm3
- 1232000 cm3
681 cm3

6.81 cm3

**Q.**

The base of radii of 2 right circular cone of same height are in the ratio of 3:5. Find the ratio of volume

**Q.**

The volume of a right circular cone of height 12 cm and base radius 6 cm, is

(a) (2π)cm3 (b) (36π)cm3 (c) (72π)cm3 (d) (144π)cm3

**Q.**

A hemispherical tank is emptied by a pipe at the rate of 5 litres per minute. How long will it take to half-empty the tank if its diameter is 112 m.

**Q.**Question 2 (ii)

Find the capacity in litres of a conical vessel with:

(ii) height 12 cm, slant height 12 cm.

[Assume π=227]

**Q.**

Water is flowing at the rate of $3km/h$ through a circular pipe of $20cm$ internal diameter into a circular cistern of diameter $10m$ and depth $2m$. In how much time, will the cistern be filled?

**Q.**

Question 1 (ii)

Find the volume of the right circular cone with:

(ii) radius 3.5 cm, height 12 cm

[Assume π=227]

**Q.**

How many silver coins, $1.75cm$ in diameter and thickness $2mm$, must be melted to form a cuboid of dimensions $5.5cm\times 10cm\times 3.5cm$?

**Q.**If h, C, V are respectively the height, the curved surface and volume of a cone, prove that 3πVh3−C2h2+9V2=0. [4 MARKS]

**Q.**

The height of a cone is 15 cm. If its volume is 1570 cm^{3}, find the diameter of its base. [Use π = 3.14]

**Q.**

The volume of a right circular cone of radius 30 cm and slant height 50 cm is

37000 cm

^{3 }37560 cm

^{3}37080 cm

^{3}37680 cm

^{3 }

**Q.**

Find the volume, curved surface area and the total surface area of a cone whose height is 6 cm and slant height 10 cm.(Take π=3.14)

**Q.**

The volume of an ice cream cone of top radius 3 cm and slant height 5 cm is(use π=3.14)

35.48 cm

^{3}30.68 cm

^{3}37.68 cm

^{3}36.58 cm

^{3}

**Q.**For the question given below, four alternative choices have been provided of which only one is correct. You have to select the correct choice:

The diameter and height of a right circular cone are 7 cm and 12 cm, respectively. The volume of the cone (in cm

^{3}) is:

(a) 88

(b) 112

(c) 154

(d) 616