Shape Conversion of Solids

Q.

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

Q. A solid cylinder of diameter 12 cm and height 15 cm is melted and recast into toys with the shape of a right circular cone mounted on a hemisphere of radius 3 cm.If the height of the toy is 12 cm, find the number of toys so formed.

Q.

A solid metallic sphere of diameter 8 cm is melted and drawn into a cylindrical wire of uniform width. If the length of the wire is 12 m, find its width.

Q.

A hollow sphere of external and internal diameters 8 cm and 4 cm respectively is melted into a solid cone of base diameter 8 cm. Find the height of the cone.

Q.

A well of diameter 2 m is dug 14 m deep, The earth taken out of it is spread evenly all around it to form an embankment of height 40 cm. Find the width of the embankment.

Q.

How many balls each of radius 1 cm can be made by melting a bigger ball whose radius is 8 cm?

1. 456

2. 512

3. 868

4. 984

Q.

A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is melted and cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. The length of the pipe will be

1. 112 m

2. 120 m

3. 130 m

4. 102 m

Q.

A hemospherical bowl of internal radius 9 cm is full of liquid. This liquid is to be filled into cylindrical shaped small bottles each of diameter 3 cm and height 4 cm. How many bottles are necessary to empty the bowl ?

Q.

A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each of diameter $4\frac{2}{3}$ cm and height 3 cm. Find the number of cones so formed.

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. 5.0 m

2. 2.81 m

3. 3.95 m

4. 2.5 m

Q.

The rain water from a roof of dimensions $22m\times 20m$ drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m If the rain water collected from the roof just fills the cylindrical vessel, then find the rain fall in cm.

Q.

Question 12
Twelve solid spheres of the same size are made by melting a solid metallic cylinder of base diameter $2cm$ and height $16cm$. the diameter of each sphere is
(A) $4cm$
(B) $3cm$
(C) $2cm$
(D) $6cm$

Q.

A solid cuboid of iron with dimensions $53cm\times 40cm\times 15cm$ is melted and recast into a cylindrical pipe. The outer and inner diameters of pipe are 8 cm and 7 cm respectively. Find the length of pipe.

Q. A metallic sphere of radius 4.2 cm is melted and recast into a cylinder of radius 6 cm. Find the height of the cylinder.

1. 2.744 cm
2. 4.818 cm
3. 5.822 cm
4. 6.136 cm

Q. How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimensions 66 cm, 42 cm and 21 cm.

1. 1600
2. 1200
3. 1900
4. 1500

Q.

A copper rod of diameter 1 cm and length 8 cm is draw into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Q.

What length of a solid cylinder 2 cm in diameter must be taken to recast into a hollow cylinder of length 16 cm, external diameter 20 cm and thickness 2.5 mm?

Q. A sphere of radius 16 cm is melted and moulded to n spheres of radius 4 cm. Here, n =

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

Q.

Rain water, which falls on a flat rectangular surface of length 6 m and breadth 4 m is transferred into a cylindrical vessel of internal radius 20 cm. What will be the height of water in the cylindrical vessel if a rainfall of 1 cm has fallen ?

Q. Question 17
During conversion of a solid from one shape to another, the volume of the new shape will
(A) increase
(B) decrease
(C) remain unaltered
(D) be doubled

Q.

A metal cuboid of dimension $22cm\times 15cm\times 7.5cm$ was melted and cast into a cylinder of height $14cm$ . What is the radius of the cylinder?

Q. In a rain-water harvesting system, the rain-water from a roof of 22 m $\times$ 20 m drains into a cylindrical tank having diameter of base 2 m and heigth 3.5 m. If the tank is full, find the rainfall in cm. Write your views on water conservation.

Q.

A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.

Q.

A conical flask is full of water. The flask has base-radius r and height h. The water is poured into a cylindrical flask of base-radius mr. Find the height of water in the cylindrical flask.

Q.

A spherical cannon ball 28 cm in diameter is melted and recast into a right circular conical mould, base of which is 35 cm in diameter. Find the height of the cone.

Q.

Metallic spheres of radii 6 cm, 8 cm, and 10 cm, respectively, are melted to form a single solid sphere. Find the radius of the resulting sphere.

Q.

The $\frac{3}{4}$th part of a conical vessel of internal radius 5 cm and height 24 cm is full of water.The water is emptied into a cylindrical vessel with internal radius 10 cm. Find the height of water in cylindrical vessel.

Q.

A cistern, internally measuring $150cm\times 120cm\times 100cm$, has $129600c{m}^3$ of water in it. Porous bricks are placed in the water until the cistern is full to the brim. Each brick absorbs one-seventeenth of its own volume of water. How many bricks can be put in without overflowing the water, each being$22.5cm\times 7.5cm\times 6.5cm$ ?

Q.

A cone of height 20 cm and radius of base 5 cm is made up of modelling clay. A child reshapes it in the form of a sphere. Find the diameter of the sphere.

Q.