Volume of a Right Circular Cone

Q. The height and the slant height of a cone 21 cm and 28 CM respectively find the volume of the cone.

Q.

The volume of a conical tent is 1232 $m^3$ and its base area is 154 $m^2$. The length of the canvas required to cover this conical tent if its width is 2 m will be:

1. 295 m

2. 275 m

3. 550 m

4. 725 m

Q.

A sphere, a cylinder, and a cone are of the same radius and same height.(Radius is equal to height). Find the ratio of their volumes.

1. $1:2:3$

2. $4:3:1$

3. $2:3:2$

4. $2:1:3$

Q.

If radius and height of a cone is increased by 10% then find the volume of cone.

Q.

Ratio of volume of cone and a cylinder of base of same radius and same height is:

1. 1 : 3

2. 1 : 1

3. 1 : 4

4. 1 : 2

Q. The volume of a cone is is 462cm ^3 of its base radius is 7 cm, then its height is

Q.

The height of a cone is 15 cm.If its volume is 500$\pi c{m}^3$, then find the radius of its base.

Q. Question 7
A joker’s cap is in the form of a right circular cone of base radius 7 cm and height 24 cm. Find the area of the sheet required to make 10 such caps. $[Assume\pi =\frac{22}{7}]$

Q.

Please help with the below question

a cone and a sphere have equal radii and equal volume. Find the relation between the radius (r) and the height (h) of the cone

Q. A conical flask of height 24 cm and curved surface area is 550 CM square. find the volume.

Q.

The volume of a cone whose height and radius is 6 cm and 5 cm respectively is:

1. 45π

2. 50π

3. 55π

4. 40π

Q. Question 6 (i)
The volume of a right circular cone is $9856c{m}^3$. If the diameter of the base is 28 cm, find:
(i) height of the cone.
$[Assume\pi =\frac{22}{7}]$

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. If the radius of the base of a right circular cone is 3r and its height is equal to the radius of the base, then its volume is

(a) $\frac{1}{3}{\mathrm{\pi r}}^3$

(b) $\frac{2}{3}{\mathrm{\pi r}}^3$

(c) $3{\mathrm{\pi r}}^3$

(d) 9${\mathrm{\pi r}}^3$

Q. A sphere, a cylinder and a cone have the same diameter. The height of the cylinder and also the cone are equal to the diameter of the sphere. Find the ratio of their volumes.

Q.

Pavan built a conical flask using 550 $m^2$ of aluminium sheet. If the radius of the flask is 7 m, then how much water can be filled in the flask(in litres)? [The bottom of the flask is of another material.]

1. 1232 litres

2. 1232000 litres

3. 12300 litres

4. 123 litres

Q. If the volume and radius of the cone are $320\pi c{m}^3$ and $8cm$ respectively then find the total surface area of the cone.

Q.

The radius and height of a cone are in the ratio 4: 3. The area of the base is 154 cm². The area of the curved surface in $c{m}^2$ is

1. 192.5

2. 190.5

3. 182.5

4. 162.5

Q. The curved surface area of a cylindrical pillar is 264 sq. m and its volume is 924 cub. m. Find the ratio of its diameter to its height.

1. 3 : 7
2. 7 : 3
3. 6 : 7
4. 7 : 6

Q. Question 1
Diameter of the base of a cone is 10.5 cm and its slant height is 10 cm. Find its curved surface area. $[Assume\pi =\frac{22}{7}]$

Q.

An ice-cream machine has two taps for filling ice-cream cones of height 6 cm and radius 3 cm. If the flow rate of ice-cream from both taps is equal to 2 $c{m}^3{s}^{-1}$. Find the maximum number of cones machine can fill in an hour.

1. 248

2. 255

3. 260

4. 258

Q. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recasted into 10 smaller cones of radius 1.4 cm. Find the height of the smaller cones formed.

1. $h=1.89cm$
2. $h=1.54cm$
3. $h=1.72cm$
4. $h=1.79cm$

Q. If volume of a cone is $1212c{m}^3$ and its height is $24cm$. Find the surface are of the cone $(\pi =\frac{22}{7})$

1. $8081.41c{m}^2$
2. $8881.41c{m}^2$
3. $881.41c{m}^2$
4. $808.41c{m}^2$

Q. The radius and height of a right circular cone are in the ratio $5:12$ and volume is $2512cm$, then find the curved surface area and the total surface area of the cone is

1. $1140.33{cm}^2$
2. $1150.42{cm}^2$
3. $1130.56{cm}^2$
4. $1125.59{cm}^2$

Q. Volume of a cylinder = 36 cm${}^3$, then volume of cone having same height and radius = .

1. 12 cm${}^3$
2. 18 cm${}^3$
3. 9 cm${}^3$

Q. The height of a cone is $15$cm. If its volume is $1570$ cm${}^3$, find the radius of the base.

Q. Calculate the volume of a cone if the height is $22$ cm and radius is $14$ cm . (Assume $\pi =\frac{22}{7}$)

1. $4517.33{cm}^3$
2. $4527.33{cm}^3$
3. $4507.33{cm}^3$
4. $4506.33{cm}^3$

Q. A steel cylinder of $40$ litres capacity contains a gas under $100$ atmosphere pressure. Find how many cylinders of $400{cm}^3$ capacity could be filled from it at $76cm$ of $Hg$?

1. 10, 000
2. 40, 000
3. 1, 000
4. 4, 000

Q. A conical tent is to accommodate 11 persons. Each person must have 4 m² of the space on the ground and 20 m³ of air to breath. Find the height of the cone.

Q. Find the volume of the right circular cone with
(i) radius $6cm$, height $7cm$.
(ii) radius $3.5cm$, height $12cm$