Conversion of Solids

Q.

Metallic spheres of radii 6cm, 8cm and 10cm, respectively are melted to form a single solid sphere. The radius of the resulting sphere(in cm) is

1. 24

2. 18

3. 15

4. 12

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 $345c{m}^3$ ^. Check whether she is correct, taking the above as the inside measurements, and $\pi =3.14$. [4 MARKS]

Q.

Assertion : A shot put is metallic sphere of radius $4\mathrm{cm}$. If the density of the metal is $10\mathrm{g}$ per ${\mathrm{cm}}^3$, then the mass of the shot put is $2\mathrm{kg}$.

Reason: Volume of sphere of radius $r$ is $\frac{4}{3}\pi r^3$.

Which of the following is correct?

1. If both assertion and reason are true and reason is the correct explanation of assertion.

2. If both assertion and reason are true but reason is not the correct explanation of assertion.

3. If assertion is true but reason is false.

4. If assertion is false but reason is true.

Q.

In Akshita’s house there is a flower pot. The sum of radii of circular top and bottom of a flowerpot is 140 cm and the difference of their circumference is 88 cm. Find the diameter of the circular top and bottom. [4 MARKS]

Q.

Inner radius of a hollow iron sphere is 9 cm. If Iron is 1 cm thick, find the volume of iron used to make the ball.

1. 1155.08 cm³

2. 1134.59 cm³

3. 1156.08 cm³

4. 1133.58 cm³

Q. The base radius and height of a right circular solid cone is 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the numbers of spheres so formed.

1. 32
2. 16
3. 20
4. 64

Q.

A juice seller fills glasses from a big cylindrical container of height $35.2cm$ and radius $10cm.$ He charges $\text{Rs.}10$ for each glass of height $10cm$ and $4cm$ radius. The amount of money he earns by selling juice is $(\text{Take}\pi =\frac{22}{7})$

1. Rs.110

2. Rs.220

3. Rs.170

4. Rs.190

Q.

A cylindrical jar of radius $12cm$ contains oil. Iron spheres each of radius $3cm$ are immersed in the oil. How many such spheres are needed to raise the oil by $4cm$?

1. 16

2. 8

3. 10

4. 32

Q. A cone of radius 7 cm and height 28 cm is recast into following shapes. Pair the radius in each case.

1. 7 cm
2. 3.5 cm
3. 213 cm

Q.

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of $\pi$. [2 MARKS]

Q. A juice seller sells juice from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges ₹ 10 for each cylindrical glass of juice whose height is 10 cm and radius is 4 cm. Find the total amount of money he earns by selling the juice.(Take $\pi =\frac{22}{7}$)

Q. A spherical clay model of diameter 12cm is moulded into a frustum by a professional engineer with diameters 15cm and 10cm. What will be the slant height of the frustum obtained (in cm)?

1. 18.187

Q. If a rectangular box of length 14 cm, breadth 22 cm, and height 14 cm is converted into a cylindrical box whose height is 7 cm, then find the radius of the converted cylindrical box.

1. $13cm$
2. $14cm$
3. $15cm$
4. $16cm$

Q. A cone of radius 3 m and height 12 m is recasted into following shapes. Pair the radius in each case.

1. $3\times \sqrt[3]{32}m$
   
2. $2\sqrt{3}m$
3. $3m$

Q.

The radii of the internal and external surfaces of a metallic spherical shell are 3 cm and 5 cm respectively. It is melted and recast into a solid right circular cylinder of height $10\frac{2}{3}cm$. Find the diameter of the base of the cylinder.

Q.

A juice seller fills glasses from a big cylindrical container of height 35.2cm and radius 10cm. He charges Rs 10 for each glass of height 10 cm and 4 cm radius. The amount of money he earns by selling juice is: (Take $\pi$= $\frac{22}{7}$)

1. Rs.110

2. Rs.220

3. Rs.170

4. Rs.190

Q.

Question 2
A rectangular water tank of base $11m\times 6m$ contains water upto a height of 5 m. If the water in the tank is transferred to a cylindrical tank of radius 3.5 m, find the height of the water level in the tank.

Q.

A shopkeeper sells lemon juice. He fills glasses from a big cylindrical container of height 35.2 cm and radius 10 cm. He charges Rs. 10 for each glass of height 10cm and 4cm radius. Find the amount of money he earns by selling juice. (Take $\pi$= $\frac{22}{7}$)

Q. The base radius and height of a right circular solid cone is 12 cm and 24 cm respectively. It is melted and recast into spheres of diameter 6 cm each. Find the numbers of spheres so formed.

1. 64
2. 32
3. 16
4. 20

Q.

A rectangular sheet of size 22 cm × 10 cm is folded along its length to form a cylinder. Find the volume of the cylinder formed in ${cm}^3$.

Q. A cone of height 36 cm and base radius 9 cm is reshaped into a sphere. Find the radius of the sphere formed.

1. 9 cm
2. 10 cm
3. 8 cm
4. 15 cm

Q. Question 18
Water flows through a cylindrical pipe, whose inner radius is 1 cm, at the rate of 80 cm/sec in an empty cylindrical tank, the radius of whose base is 40 cm. What is the rise of water level in tank in half an hour?

Q. A hollow cylindrical iron pipe is of length $28cm$. Its outer and inner diameters are $8cm$ and $6cm$ respectively. Find the volume of the pipe and weight of the pipe if $1cu.cm$ of iron weighs $7gm$. (Take $\pi =\frac{22}{7}$)

Q. If a cone of radius 15 cm and height 60 cm is melted and recast to form a sphere, then radius of sphere = .

1. 15 cm
2. 10 cm
3. 16 cm
4. 12 cm

Q. A cone of height 24 cm and radius of base 6 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the radius of the sphere.

Q. The volume of a largest sphere that can be cut from cylindrical log of wood of base radius $1m$ and height $4m$ is:

1. $\frac{8}{3}\pi m^3$
2. $\frac{10}{3}\pi m^3$
3. $\frac{16}{3}\pi m^3$
4. $\frac{4}{3}\pi m^3$

Q. When we combine many solids of same material to form one single solid, which of the following remains constant?

1. Volume
2. Surface area
3. Perimeter
4. Curved Surface Area

Q. A cone of radius 3 m and height 12 m is recasted into following shapes. Pair the radius in each case.

1. $3\times \sqrt[3]{32}m$
   
2. $2\sqrt{3}m$
3. $3m$

Q. A cylindrical bucket of height 10 cm and radius 5 cm is overturned to form a conical heap of sand of radius 5 cm. Find the height of the cone.

1. 30 cm
2. 20 cm
3. 10 cm
4. 40 cm

Q. If a cone of radius 15 cm and height 60 cm is melted and recast to form a sphere, then radius of sphere = .

1. 10 cm
2. 15 cm
3. 12 cm
4. 16 cm