# Shape Conversion of Solids

## Trending Questions

**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?

456

512

868

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

112 m

120 m

130 m

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 423 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.

5.0 m

2.81 m

3.95 m

2.5 m

**Q.**

The rain water from a roof of dimensions 22 m×20 m 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 53 cm×40 cm×15 cm 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.

- 2.744 cm
- 4.818 cm
- 5.822 cm
- 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.

- 1600
- 1200
- 1900
- 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 =

- 16
- 4
- 64
- 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 × 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 34th 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.**