Volume Questions

The number of balls of radius $2\text{cm}$ that can be made from a solid sphere of radius $4\text{cm}$ is:

A right triangle with sides 5cm,12cm and 13cm is rotated about the side 12cm to form a cone. The volume of the cone so formed is:

A hollow copper pipe is 22cm long and its external diameter is 28cm. If the thickness of the pipe is 3cm and iron weighs 8.5g/cm
3
, then the weight of the pipe is closest to:

The height of a cylinder and its volume are 15cm and 2310cm
3
, respectively. Find the total surface area.

The height of one cone is 3 times the height of another cone, while its radius is half of the radius of the other cone. If their total volume is 100unit
3
, then the difference in the volumes of the cones is _______ unit
3
.

If the percentage increase in the radius of a cylinder is $300\%$, then by what percentage does the volume of the cylinder change, keeping the height of the cylinder constant?

Three cubes of edges $6\text{cm}$, $8\text{cm}$ and $10\text{cm}$ are melted without loss of metal into a single cube. The edge of the new cube will be:

A right circular cone, a right circular cylinder and a hemisphere all have the same radius, and the heights of the cone and cylinder equal their diameters. Then their volumes are proportional respectively to:

Three solid spheres of gold whose radii are $1\text{cm}$, $6\text{cm}$ and $8\text{cm}$ respectively are melted into a single solid sphere. Then the radius of the sphere is:

A conical container of base diameter $2R$ and height $H$ is full of water which is poured into a cylindrical container of diameter $2pR$. Then it will occupy a height equal to:

A hemispherical can with an internal radius of $9\text{cm}$ is completely filled with water. Someone is requested to fill this water into cylindrical bottles, each with a diameter of $3\text{cm}$ and a height of $4\text{cm}$. The number of bottles required to empty the can is:

An article is of size 9cm×6cm×3cm. The number of such articles that can be packed in a box measuring 63cm×42cm×21cm is:

A cube has a surface area of 5400square units. Its volume would increase approximately _______ if the side is increased by 5units.

How many cubes of length 50 cm can be accommodated in a container of 5 m in length, 2 m in width and 5 m in height?

The radius of a hemisphere is 9cm. Its volume will be:

The radii of the two spheres are in the ratio 4:3. What is the ratio between their volumes?

The volume of a solid sphere is 4851 m
3
. What is the surface area of the sphere? (Take π=
7
22
​
)

A solid metallic sphere of radius 4 cm is melted and recast into 4 identical cubes. What is the side of the cube?

The dimensions of a pond are 20m, 14m and 6m. Find the capacity of the pond.

The radius and height of a cylinder are in the ratio 7:13 and its volume is 6006 cm
3
. Its radius will be: (Use π=
7
22
​
)