Volume of a right circular cone

Q.

From each end of a solid metal cylinder, metal was scooped out in hemispherical form of same diameter. The height of the cylinder is $10cm$ and its base is of radius $4.2cm$. The rest of the cylinder is melted and converted into a cylindrical wire of $1.4cm$ thickness. Find the length of the wire.

Q.
Observe the measures of pots In the given figure. How many jugs of water can the cylindrical pot hold?

Q. Total surface area of a solid hemisphere is 4158cm², the diameter of the hemisphere is equal to __________ cm.
(Take $\pi$ = $\frac{22}{7}$)

1. 20
2. 21
3. 40
4. 42

Q. Question 7
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

Q. A solid wooden toy is in the shape of right circular cone mounted on a hemisphere of radius $4.2cm$. The total height of the toy is $10.2cm$ find the volume of the toys.

Q. Find, correct to three significant figures, the radius of the base of a circular cone whose height is 5 cm and volume 12 cm³.

Q. A right circular cone is $5.8cm$ high and radius of its base is $3.4cm$. It is melted and recast into a right circular cone with radius of its base $1.7cm$. Find its height.

1. $20.2cm$
2. $21.2cm$
3. $23.2cm$
4. $22.2cm$

Q. The volume of solid right cylinder cone is $4928cu.cm$. If a height is $24cm$, then find the radius of the cone. (Take $\pi =\frac{22}{7}$)

Q. If the height and radius of a cone are doubled, then the value of the cone becomes:

1. $2$ times
2. $4$ times
3. $6$ times
4. $8$ times

Q.

Question 7
A solid consisting of a right circular cone of height 120 cm and radius 60 cm standing on a hemisphere of radius 60 cm is placed upright in a right circular cylinder full of water such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is 60 cm and its height is 180 cm.

Q. A cone, a right circular cylinder and a hemisphere standing on equal base and have same height. What is the ratio of their volumes ?

1. $2:3:1$
2. $1:2:3$
3. $2:1:3$
4. $1:3:2$

Q. The radii of three cylindrical jars of equal height are in the ratio $1:2:3$. Second jar is full with water which is first poured into the first jar. After fiiling the first jar, water is poured into the third jar. Which of the following statements is true ?

1. Third jar is half full
2. Third jar is two thirds full
3. Third jar is one third full
4. Third jar is four ninths full

Q. The radius and height of a cone are each increased by $20$, then the volume of the cone is increased by

1. $20$
2. $40$
3. $60$
4. $72.8$

Q.

An ice cream cone has a radius of 3 cm and a height of 12 cm. A half scoop of ice cream is placed on the cone. If the ice cream melts, will it fit into the cone? [2 MARKS]

Q. The trunk of a tree is a right cylinder $1.5m$ in radius and $10m$ high. What is the volume of the timber which remains when the trunk is trimmed just enough to reduce it to a rectangular parallelogram on a square base?

1. $45m^2$
2. $54m^2$
3. $50m^2$
4. $48m^2$

Q. There are two vessels - one is in the shape of a cylinder and the other in the shape of a right circular cone. Both the vessels have the same height and the same base radius. The cylindrical vessel and the conical vessel are filled with milk and water respectively and are both filled to half of their maximum heights. The cone is standing on its vertex. The contents of the conical vessel are emptied into the cylindrical vessel. What is the ratio of water to milk in the cylindrical vessel now -

1. 1 : 4
2. 1 : 9
3. 1 : 1
4. 1 : 3

Q. A heap of rice is in the form of cone of diameter 24 m and height 3.5 m. Find the volume of rice. How much canvas cloth is required to cover the heap?

Q. How many spherical bullets can be made out of a lead cylinder $15$cm high and with base radius $3$cm, each bullet being $5$mm in diameter?

1. $6000$
2. $7260$
3. $6480$
4. $7800$

Q. If $h,c$ and $v$ respectively, are the height, the curve surface and volume of the cone, then
$3\pi v{h}^3-c^2{h}^2+8v^2=0$

1. True
2. False

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

1. 300%
2. 200%
3. 100%
4. 400%

Q. Two cones $A$ and $B$ have their base radii in the ratio of $4:3$ and their heights in the ratio $3:4$. The ratio of volume of cone $A$ to that of cone $B$ is

1. $4:3$
2. $3:4$
3. $2:3$
4. $1:2$

Q.

Radii of base of cylinder and cone are in the ratio 3:4 and heights in ratio 2:3 . Find ratio of their volumes.