Volume of Regular Solids

Q.

Parikshit makes a cuboid of plasticine of sides $\mathit{5}\mathrm{cm},\mathit{2}\mathrm{cm}\mathrm{and}\mathit{5}\mathrm{cm}$. How many such cuboids will he need to form a cube?

Q. A solid consists of a circular cylinder with an exact fitting right circular cone placed on the top. The height of the cone is h. If the total volume of the solid is three times the volume of the cone, then the height of the cylinder is

1. $2h$
2. $4h$
3. $\frac{2h}{3}$
4. $\frac{3h}{2}$

Q.

Find the volume of a sphere whose radius is 7 cm
$[Assume\pi =\frac{22}{7}]$

1. $1437.33c{m}^3$

2. $1500c{m}^3$

3. $1600.33c{m}^3$

4. $1750.33c{m}^3$

Q.

Obtain the volume of rectangular boxes with the following length, breadth and height respectively.

$5a,3a^2,7a^4$

Q. An iron cylinder of length $10\text{cm}$ has a diameter of $8\text{cm}$. What is the volume of the cylinder?

1. $500.24{\text{cm}}^3$
2. $500.85{\text{cm}}^3$
3. $502.85{\text{cm}}^3$
4. $2011{\text{cm}}^3$

Q.

How many $c{m}^3$ of milk can a hemispherical bowl of diameter 10.5 cm hold?
$[Assume\pi =\frac{22}{7}]$

Note : Hemisphere is half a sphere.

1. $301.1875c{m}^3$

2. $304.1875c{m}^3$

3. $303.1875c{m}^3$

4. $302.1875c{m}^3$

Q. A cuboid shaped container has volume (4xy^5z^5 – 20x^2y^3z^3 + 25x^3yz) cu. metres and height (2y^2z^2 – 5x) m. Find the area of the base of the cuboidal container.

Q. What is the ratio of volume of sphere to that of the cone?
I. Radius of the cone is twice that of the sphere.

II. Height of the cone is equal to the radius of the sphere.

1. if the question can be answered by using either of the statements alone.
2. if the question can be answered only by using both the statements together.
3. if the question cannot be answered.
4. if the question can be answered by using any of the statements alone but not by using the other statement alone.

Q. An iron cylinder of length $8\text{cm}$ has a diameter of $4\text{cm}$. Find the volume of the cylinder in ${\text{cm}}^3$?

1. 100.6

Q.

The radius of the sphere r is given. Find the volume of the sphere. Write your answer in terms of $\mathrm{\pi }$.

$\mathrm{r}=12\mathrm{Units}$

Q.

The radius of a sphere is $2r$, then its volume will be:

1. $\frac{4}{3}{\mathrm{\pi r}}^3$

2. $4{\mathrm{\pi r}}^3$

3. $\frac{8}{3}{\mathrm{\pi r}}^3$

4. $\frac{32}{3}{\mathrm{\pi r}}^3$

Q. A cuboid shape aquarium is $100cm$ long and $50cm$ wide. It contains water up to a height of $30cm$. Find the volume of water in $m^3$.

1. $15m^3$
2. $150c{m}^3$
3. $0.15m^3$
4. $1.5m^3$

Q.

A solid iron cuboidal block of dimensions 4.4 m × 2.6 m × 1 m is recast into a cylindrical pipe of radius 100 cm. The length of the pipe is:

1. 11.2 cm

2. 11.2 m

3. 112 cm

4. 112 m

Q. A cone of volume V and height h is converted into another cone of same height but with double area of base.The volume of new cone is kV the value of k i

Q.

An 8cm cube has a 4 cm square hole cut through its center. What is the remaining volume, in cm3?

Q.

Which is different? Find both answer.

How much does it take to fill the cylinder?

What is the capacity of the cylinder?

How much does it take to cover the cylinder?

How much does the cylinder contain?

Q. The formula for the volume of a sphere is $V=\frac{4}{3}\pi r^3$, and the formula for the surface area of a sphere is $A=4\pi r^2$. If a sphere has a surface area of $36\pi$, what is its volume?

1. $27\pi$
2. $36\pi$
3. $54\pi$
4. $72\pi$

Q. Volume of a solid cylinder is $62.37cu.cm$. Find the radius if its height is $4.5cm$.

1. $r=2.1cm$
2. $r=4.1cm$
3. $r=5.1cm$
4. None of these

Q.

A slab of iron of dimensions 60 cm x 20 cm x 28.26 cm is used to cast an iron pipe. the outer diameter of the pipe is 10 cm and the thickness is 1 cm, calculate the length of the pipe.(take pie = 3.14)

Q. If the volume of a vessel in the form of a right circular cylinder is 448 $\pi c{m}^3$ and its height is 7 cm, then the curved surface area of the cylinder is

1. $224\pi c{m}^2$
2. $212\pi c{m}^2$
3. $112\pi c{m}^2$
4. None of these