Shape conversion of solids

Q.

How many square metres of glass will be required for a window which has $6$ panes, each measuring $25cm\times 14cm$.

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. 10 cm

2. 8 cm

3. 15 cm

4. 9 cm

Q.

A 20 m deep well of diameter 7 m is dug and the earth taken out is evenly spread out to form a platform of 22 m by 14 m. Find the height of the platform.

1. 10 m

2. 2.5 m

3. 7.5 m

4. 5 m

Q.

There is a thin metal plate of length and breadth 2M mm and 2K mm respectively. Its thickness is 1mm. ‘N’ number of plates are placed one on top of the other? What is the object formed and what is its volume in ${mm}^3$ ?

1. Cuboid, MKN

2. Sphere, 4MKN

3. Cuboid, 4MKN

4. Cylinder, 2 MKN

Q.

Water flows at the rate of $10\mathrm{m}/\mathrm{minute}$ through a cylindrical pipe $5\mathrm{mm}$ in diameter. How long would it take to fill a conical vessel whose diameter at the base is $40\mathrm{cm}$ and depth $24\mathrm{cm}$?

Q.

A 20m deep well having diameter 7m is dug and the earth dug out is evenly spread to form a platform 22m by 14m. Find the height of the platform.

1. 2.5 m

2. 5.0 m

3. 2.81 m

4. 3.95 m

Q.

A cone of height h cm and base radius r cm is reshaped into a sphere. Then, which of the following is always correct?

1. Volume of cone = Volume of Sphere

2. Surface Area of Cone = Surface Area of Sphere

3. Can’t Say anything about the volume or surface area relation

4. Radius of sphere = Radius of base of cone + Height of cone

Q. A well of height 30 m and radius 14 m is dug out. The sand extracted is used to make a platform of length 10 m, breadth 14 m and height H. What is the value of H?

1. 130 m
2. 150 m
3. 180 m
4. 132 m

Q. Two cylinders A and B are formed by folding a rectangular sheet of dimensions 20 𝑐𝑚 × 10 𝑐𝑚 along its length and also along its breadth respectively. The volume of A is ________ the volume of B.

1. equal to
2. one fourth of
3. double
4. half of

Q. The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 2 mm. The length of the wire is:

1. 18 m
2. 12 m
3. 36 m
4. 66 m

Q.

A metallic sphere of radius 4.2 cm is melted and recast into the shape of a cylinder of radius 6 cm. Find the height of the cylinder (in cm).

___

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. 16
2. 20
3. 64
4. 32

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. 40 cm
3. 20 cm
4. 10 cm

Q. Water flows at the rate of 10 metre per minute from a cylindrical pipe with 5mm long diameter. How long will it take to fill up a conical vessel whose diameter is 40 cm and depth is 24 cm?

1. 48 minutes 15 secs
2. 51 minutes 12 secs
3. 52 minutes 1 sec
4. 55 minutes

Q. 21560 cubic cm of a liquid is filled in some cylindrical shaped containers of radius 7 cm and height 14 cm. Find the number of such containers required.

1. 7
2. 5
3. 10
4. 15

Q. A hemispherical bowl of internal radius 9 cm is full of liquid. The liquid is to be filled into cylindrical shaped small bottles, each of diameter 3 cm and height 4 cm. How many bottles are needed to empty the bowl?

1. 54
2. 27
3. 36
4. 18