Volume of a right circular cone

Q. Question 3
The height of a cone is 15 cm. If its volume is $1570c{m}^3$, find the radius of its base.
$[Use\pi =3.14]$

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 $(Use\pi =3.14)$

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

1. $16\pi c{m}^2$
2. $9\pi c{m}^2$
3. $12\pi c{m}^2$
4. $8\pi c{m}^2$

Q.

If the volume of a right circular cone of height 9 cm is 48 $\pi c{m}^3$, 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 $165m^2$ 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 $(Use\pi =3.14)$

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.

1. $1232c{m}^3$
2. $1232000c{m}^3$

3. $681c{m}^3$

4. $6.81c{m}^3$

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

$\left(a\right)\left(2\pi \right)c{m}^3\left(b\right)\left(36\pi \right)c{m}^3\left(c\right)\left(72\pi \right)c{m}^3\left(d\right)\left(144\pi \right)c{m}^3$

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 $1\frac{1}{2}m$.

Q. Question 2 (ii)
Find the capacity in litres of a conical vessel with:
(ii) height 12 cm, slant height 12 cm.
$[Assume\pi =\frac{22}{7}]$

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
$[Assume\pi =\frac{22}{7}]$

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 $3\pi V{h}^3-C^2{h}^2+9V^2=0$. [4 MARKS]

Q.

The height of a cone is 15 cm. If its volume is 1570 cm³, 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

1. 37000 cm³

2. 37560 cm³

3. 37080 cm³

4. 37680 cm³

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.$(Take\pi =3.14)$

Q.

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

1. 35.48 cm³

2. 30.68 cm³

3. 37.68 cm³

4. 36.58 cm³

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 cm³) is:

(a) 88

(b) 112

(c) 154

(d) 616