Q28 of 56 Page 13

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 and embankment of height 40 cm. Find the width of the embankment. (CBSE 2015)

Let us assume shape of well is like a solid circular cylinder


Radius of cylinder, r = 2/2 = 1m


Depth(height) of well, h = 14m


Volume of right circular cylinder, V’ = π r2 h


---------(I)


Given that, length of embankment, l = 40 cm


Let width of the embankment be x m


Volume of the embankment, V’’ = π r2 h


= π ((1+x)2 – 1)2 x 0.4 -----------(II)


Since well is spread evenly to form the embankment, so their volumes, V’ = V’’


⇒ π × 14 = π ((1+x)2 – 1)2 x 0.4


⇒ x = 5m


∴ Height of the embankment, x = 5cm

More from this chapter

All 56 →
26

A solid metallic sphere of radius 5.6 cm is melted and solid cones each of radius 2.8 cm and height 3.2 cm are made. Find the number of such cone formed. (CBSE 2014)

 27

A hemispherical depression is cut out from one face of a cubical wooden block such that the diameter l of the hemisphere is equal to the edge of the cube. Determine the surface area of the remaining solid (CBSE 2014)

 29

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. (CBSE 2015)

 30

The largest cone is curved out from one face of solid cube of side 21 cm. Find the volume of the remaining solid.(CBSE 2015)