Volume of Hollow Cylinder

Q.

A Thin Wire Has a Length of $21.7cm$ and Radius $0.46mm$. Calculate the Volume of the Wire To Correct Significant Figure.

Q. A hemispherical bowl of internal radius 15 cm contains a liquid. The liquid is to be filled into cylindrical-shaped bottles of diameter 5 cm and height 6 cm. How many bottles are necessary to empty the bowl?

Q. As shown in the figure, a cylindrical glass contains water. A metal sphere of diameter 2 cm is immersed in it. Find the volume of the water .

Q. water is running out of a conical funnel at the rate of 5 cubic cm per sec. If the radius of the base of the funnel is 10cm and altitude is 20 cm, find the rate at which water level is dropping when it is 5 cm from the top.

Q.

A cylindrical tub of radius 5 cm and length 9.8 cm is full of water. A solid in the form of a right circular cone mounted on a hemisphere is immersed in the tub. If the radius of the a hemisphere is 3.5 cm and height of cone outside the hemisphere is 5 cm, find the volume of the water left in the tub.

1. 616 cm³

2. 200 cm³

3. 600 cm³

4. 550 cm³

Q. A solid is in the form of a cylinder with hemispherical ends. Total height of the solid is 19 cm and the diameter of the cylinder is 7 cm. Find the volume and total surface area of the solid.

Q. A cylindrical vessel 32 cm high and 18 cm as the radius of the base, is filled with sand. This bucket is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is 24 cm, the radius of its base is

(a) 12 cm

(b) 24 cm

(c) 36 cm

(c) 48 cm

Q.

A vessel is in the form of an inverted cone. Its height is 11 cm. Its top is open and has radius of 2.5 cm. The vessel is filled with water up to the rim. When spherical lead shots of radius 0.25 cm are dropped into the vessel, ²/₅^th of the water flows out. Find the number of lead shots dropped into the vessel.

1. 550

2. 500

3. 440

4. 220

5. 350

Q.

A vessel in the form of an inverted cone is filled with water to the brim. It's height is 20 cm and diameter is 16.8 cm. Two equal solid cones are dropped in it so that they are fully submerged. As a result, one third of the water in the original cone overflows. What is the volume of each of the solid cone submerged?

Q.

The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?

Q. In a cylindrical vessel of diameter 24 cm, filled up with sufficient quantity of water, a solid spherical ball of radius 6 cm is completely immersed. Find the increase in height of water level.

Q.

A solid right cylinder cone of radius $30cm$ and height 60cm is dropped in a right circular cylinder of radius 60cm full of Water upto a height of $180$ cm. Find the rise in level of water.

Q. The height of a cone is 60 cm. A small cone is cut off at the top by a plane parallel to the base and its volume is $\frac{1}{64}th$ the volume of original cone. The height from the base at which the section is made is:

Q.

A metal place has a bore (inner diameter) of 5 cm.The pipe is 5 mm thick all around.Find the weight, in kilogram, of 2 meters of the pipe if $1c{m}^3$ of the metal weighs 7.7 g.

Q. A hollow cylindrical copper pipe is 21 dm long. If its outer and inner diameters are of 10 cm and 6 cm respectively, find the volume of the copper used in making the pipe. [Take $\pi =\frac{22}{7}$] [3 MARKS]

Q.

A hollow cylinder has solid hemisphere inward at one end and on the other end it is closed with a flat circular plate. The height of water is 10 cm when flat circular surface is downward. Find the level of water, when it is inverted upside down, common diameter is 7 cm and height of the cylinder is 20 cm.

Q. A sphere of radius 6 cm is dropped into a cylindrical vessel partly filled with water. The radius of the vessel is 8 cm. If the sphere is submerged completely, then the surface of the water rises by

(a) 4.5 cm

(b) 3

(c) 4 cm

(d) 2 cm

Q. Water is leaking from a conical funnel at the rate of 5 cm2sec.If the radius of the base of the funnel is 5 cm and its altitude is 10 cm.find the rate at which the water level is dropping when it is 2.5 cm from the top

Q.

A cylindrical can of internal diameter 21 cm contains water . A solid sphere whose diameter is 10.5 cm is lowered into the cylindrical can. The sphere is completely immersed in water . Calculate the rise in water level, assuming that no water overflows.

Q.

A well of diameter $4m$ is dug $21m$ deep. the earth taken out of its has been spread evenly all around it in the shape of a circular ring of width $3m$ to form an embankment. Find the height of the embankment.

Q. 37. A conical vessel whose height is 10m and the radius of whose base is half that of the height is being filled with a liquid at a uniform rate of 1.5 m cube/min. Find the rate at which the level of the water in the vessel is rising when it is 3m below the top of the vessel.

Q. A cylindrical vessel of radius 4 cm contains water. A solid sphere of radius 3 cm is lowered into the water until it is completely immersed. The water level in the vessel will rise by

(a) $\frac{2}{9}$ cm

(b) $\frac{4}{9}$ cm

(c) $\frac{9}{4}$ cm

(d) $\frac{9}{2}$ cm

Q. The inner diameter of a glass is 7 cm and it has a raised portion in the bottom in the shape of a hemisphere, as shown in the
figure. If the height of the glass is 16 cm, find the apparent capacity and the actual capacity of the glass.

Q. The height of a solid cylinder is 15 cm and the diameter of its base is 7 cm. Two equal conical holes each of radius 3 cm, and height 4 cm are cut off. Find the volume of the remaining solid.

Q. The height of a right circular cone is 20 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume be $\frac{1}{8}$ of the volume of the given cone, then at what height above the base is the section made? [HOTS] [CBSE 2014]

Q.

If a rectangular sheet is folded along its length to cover the curved surface of the cylinder with radius R and height H, then find the length and breadth of the rectangular sheet.

1. Length of the rectangular sheet = $\pi R$
2. Breadth of the rectangular sheet = $H$
3. Length of the rectangular sheet = $2\pi R$
   
4. Breadth of the rectangular sheet = $2H$

Q. 68. If right circular cone is seperated into 3 solids of volume V1, V2, V3 by 2 planes which are parallel to base and trisect the altitude .What is the ratio of V1:V2:V3?

Q. Find the weight of a hollow sphere of metal having internal and external diameters as 20 cm and 22 cm, respectively if 1m³ of metal weighs 21g.

Q. An iron sphere of radius a units is immersed completely contained in a right circular cone of semi-vertical angle 30, water is drained off from the cone till its surface touches the sphere. find the volume of water remaining in the cone.

Q.

A sphere of radius 6cm is dropped into a cylindrical vessel partly filled with water. The radius of vessel is 8cm. If the sphere is submerged completely, then find the increase in level of water.