Conversion of Solids from One Shape to Another
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.
- 12 m
- 18 m
- 36 m
- 66 m
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.
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:
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).
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?
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).
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?
Cuboid, 4πK2 mm3
Cylinder, 2πK2 mm3
Cylinder, 4πMK2 mm3
Sphere , 2πMK2 mm3
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?
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.