Conversion of Solids from One Shape to Another

Q.

A 32cm tall cylindrical bucket of base diameter 36cm, is filled with sand and this container is emptied on the ground forming a conical heap of sand. If the height of the heap is 24cm. Find the slant height of the heap.

1. 12$\sqrt{13}$

2. 13$\sqrt{13}$

3. 15$\sqrt{13}$

4. 12$\sqrt{15}$

Q. Find the side (in cm) of a cube whose surface area is 294 ${\text{cm}}^2$.

1. 7

Q.

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

Q.

Rubik's cube has total surface area of 54 ${cm}^2$. The area occupied by a single red tile on rubik's cube is

1. 0.25 cm²

2. 1 cm²

3. 2 cm²

4. None of these

Q.

Find the number of coins, 1.5 cm in diameter and 0.2 cm thick, to be melted to form a right circular cylinder of height 10 cm and diameter 4.5 cm.
$\left[3\right]$

Q. Find the side (in cm) of a cube whose surface area is 294 ${\text{cm}}^2$.

1. 7

Q.

A well of diameter 14m is dug 8m deep. The earth taken out of it is evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment( in cm).

1. 48.2

2. 53.3

3. 50

4. 57.5

Q.

A conical vessel of radius 6 cm and height 8 cm is completely filled with water. A sphere is lowered into the water and its size is such that when it touches the sides, it is just immersed. What fraction of water overflows?

1. 0.625

2. 0.375

3. 0.125

4. 0.875

Q.

A 15 cm tall cylindrical bucket of base diameter 6 cm, is recast to form a frustum with radii 2 cm and 4 cm. Find the height of the frustum obtained.

1. 11.75 cm

2. 14.47 cm

3. 13.21 cm

4. 12.52 cm

Q.

A solid iron rectangular block of dimensions 4.4 m, 2.6 m and 1 m is cast into a hollow cylindrical pipe of internal radius 30 cm and thickness 5 cm. Find the length of the pipe (in m).

1. 112

2. 221

3. 121

4. 211

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

Q.

There is a thin coin of radius 2K mm and thickness 1 mm. Now I place M coins one on top of the other. What is the object formed and what is its volume?

1. Cuboid, 4$\pi K^2$ $m{m}^3$

2. Cylinder, 2$\pi K^2$ $m{m}^3$

3. Cylinder, 4$\pi M{K}^2$ $m{m}^3$

4. Sphere , 2$\pi M{K}^2$ $m{m}^3$

Q.

A well of diameter 14m is dug 8m deep. The earth taken out of it is evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment( in cm).

1. 48.2

2. 53.3

3. 50

4. 57.5

Q.

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

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?

1. 6.524 cm

2. 8.4 cm

3. 5.212 cm

4. 18.187 cm

Q.

12 spheres of the same size are made by melting a solid cylinder of diameter 16 cm and height 2 cm. The diameter of each sphere is:

1. $\sqrt{3}cm$

2. $2cm$

3. $3cm$

4. $4cm$