Volume of Combination of Solids

Q. A conical vessel, with base radius 5 cm and height 24 cm, is full of water. This water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to which the water will rise in the cylindrical vessel. (Use $\pi =\frac{22}{7}$)

Q.

Find the amount of water displaced by a solid spherical ball of diameter $4.2m,$ when it is completely immersed in water.

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.

Which geometric shape has the minimum surface area for a given volume?

1. Cylinder

2. Sphere

3. Cone

4. Cube

Q.

Question 9
A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1m is recast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

Q.

Anita buys a new salt cellar in the shape of a cylinder topped by a hemisphere as shown below. The cylinder has a diameter of 6 cm and a height of 10 cm. She pours the salt into the salt cellar, so that it takes up half the total volume of the cellar. Find the depth of the salt, marked with x in the diagram

1. 3 cm

2. 6 cm

3. 12 cm

4. 9 cm

Q.

A toy in shape of a hemisphere of radius 14 cm is surmounted by a cone of height 22 cm. Find the approximate volume of the toy.

1. $10266.66{\text{cm}}^3$

2. $17266.67{\text{cm}}^3$

3. $15266.67{\text{cm}}^3$

4. $12266.67{\text{cm}}^3$

Q. Find the volume of water in a solid bottle in the form of cylindrical bottom and conical top. The cylinder is of radius 2.1 cm and height 14 cm . The height of the cone is 9 cm.

1. $200.62{\text{cm}}^3$
2. $235.62{\text{cm}}^3$
3. $135.62{\text{cm}}^3$
4. $230.62{\text{cm}}^3$

Q. Question 17
A solid right circular cone of height 120 cm and radius 60 cm is placed in a right circular cylinder full of water of height 180 cm such that it touches the bottom. Find the volume of water left in the cylinder, if the radius of the cylinder is equal to the radius of the cone.

Q. Question 2
Rachel, an engineering student, was asked to make a model shaped like a cylinder with two cones attached at its two ends by using a thin aluminium sheet. The diameter of the model is 3 cm and its length is 12 cm. If each cone has a height of 2 cm, find the volume of air contained in the model that Rachel made. (Assume the outer and inner dimensions of the model to be nearly the same.)

Q. A Bangle of inner radius 2.1 cm and thickness 0.7 cm and height 0.5 cm. Find the volume of material used for bangle.(approx)

1. $2.5{\text{cm}}^3$
2. $15.8{\text{cm}}^3$
3. $10.40{\text{cm}}^3$
4. $5.4{\text{cm}}^3$

Q. The volume of water can be filled in a hollow sphere ball containing cube shape lighting device is_

1. Volume of Sphere + Volume of Cube
2. Volume of Sphere - Volume of Cube
3. Volume of Sphere × Volume of Cube
4. Volume of Sphere

Q.

Pavan filled water in a cylindrical vessel of radius 7 cm and height 14 cm. Then he gently dropped a spherical ball of radius 0.7 cm. Find the height the water will be raised to when the spherical ball is dropped into it?

1. $0.93\times {10}^{-2}\text{cm}$
2. $0.5\times {10}^{-2}\text{cm}$
3. $0.6\times {10}^{-2}\text{cm}$
4. $0.93\times {10}^{-2}\text{cm}$

Q. Match the following solid objects with the expressions of their volume.

1. ${\mathrm{\pi r}}^{2}h-\frac{1}{3}{\mathrm{\pi r}}^{2}h$
2. ${\mathrm{\pi r}}^{2}h+\frac{2}{3}{\mathrm{\pi r}}^3$
3. $2{{\mathrm{\pi r}}_1}^2{h}_1+{{\mathrm{\pi r}}_2}^2{h}_2$

Q. 32.Sa of cube is equal to sa of sphere. Find the ratio of their volumes

Q. A cistern $6m$ long and $4m$ wide contains water up to the depth of $1m25cm$. The total area of the wet surface is :

1. $49m^2$
2. $50m^2$
3. $53.5m^2$
4. $55m^2$

Q.

The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

1. 

2. 

3. 

4. 

Q.

From a solid cylinder of height 14 cm and base diameter 7 cm, two equal conical holes each of radius 2.1 cm and height 4 cm are cut off. Find the volume of the remaining solid.

Q. A tent is of the shape of a right circular cylinder upto height of $3$ metres and then becomes a right circular cone with maximum height of $13.5$ metres above the ground. Calculate the cost of painting the inner side of the tent at the rate of Rs.$2$ per square metre, if the radius of the base is $14$ metres.

1. Rs.$2068$
2. Rs.$1268$
3. Rs.$1988$
4. Rs.$2248$

Q.

The ratio of the volume of a cube to that of a sphere which will exactly fit inside the cube is

1. 

2. 

3. 

4. 

Q. A solid object made up of wood is in the shape of a cylinder with 4 cuboidal depressions. The radius and height of the cylinder is 7 cm and 10 cm, respectively. The dimensions of the cuboid are 2 cm $\times$ 3 cm $\times$ 4 cm. Find the volume of wood in the solid object.

1. $3918c{m}^3$
2. $7024c{m}^3$
3. $1444c{m}^3$
4. $789c{m}^3$

Q.

A container shaped like a right circular cylinder having diameter 12 cm and height 15 cm is full of ice cream. The ice cream is to be filled into cones of height 12 cm and diameter 6 cm, having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.

1. 30

2. 25

3. 20

4. 10

Q.

Two solid cones A and B are placed in a cylindrical tube as shown in the figure below. The ratio of their capacities is 2:1. Find the volume of the remaining portion of the cylinder.

1. $386{cm}^3$

2. $376{cm}^3$

3. $396{cm}^3$

4. $406{cm}^3$

Q.

The formula for the volume V of a sphere is given as $V=\frac{4}{3}\pi r^3$.
a) Find V if $r=5cm$.
b) Make r the subject of the formula.
c) Find the radius of a sphere of volume 2500 m³.

Q. The volume of a metal sphere increases by 0.24% when its temperature is raised by 40°C. The coefficient of linear expansion of the metal is _____________°C.
(A) 2 × 10^–5 (B) 6 × 10^–5 (C) 18 × 10^–5 (D) 1.2 × 10^–5

Q.

what is the formula of volume of solid spare and hollow spare?

Q. How many square metres of canvas are required for a conical circus tent whose height is $35$ metres and the radius of the base is $84$ metres?

Q. A spherical glass vessel has a cylindrical neck 8 cm long, 2 cm in diameter; the diameter of the spherical part is 8.5 cm. By measuring the amount of water it holds, a child finds its volume to be 345 $c{m}^3$. Check whether she is correct, taking the above as the inside measurements, and $\pi$ = 3.14

1. Yes
2. Less Data
3. No
4. None of the above

Q. A store room in the form of a cuboid has dimensions $42m\times 35m\times 21m.$ How many cuboidal boxes can be stored in it if the volume of each box is $0.7m^3?$

1. 30870
2. 44000
3. 44100
4. 4200

Q.

A vessel is in the form of an inverted cone. Its height is 8 cm and the radius of its top, which is open, is 5 cm. It is filled with water up to the brim. When lead shots, each of which is a sphere of radius 0.5 cm are dropped into the vessel, one-fourth of the water flows out. The number of lead shots dropped in the vessel is ______.

1. 100

2. 50

3. 20
4. 10