MEDIUM
10th Manipur Board
IMPORTANT
Earn 100

A cylinder is cut lengthwise and flattened, thereby forming a rectangle of dimensions 66 cm×28 cm. Find the curved surface area and volume of the original cylinder.

Important Questions on Mensuration

HARD
10th Manipur Board
IMPORTANT
A sector of a circle of radius 6 cm has angle 120°. It is rolled up so that two bounding radii are joined together to form a cone. Find the volume of the cone (decimal form).
MEDIUM
10th Manipur Board
IMPORTANT
 A conical flask of radius x units and height 2x units, is full of water. The water is poured into a cylindrical flask of radius 2x/3 units. Find the height of water in the cylindrical flask.
MEDIUM
10th Manipur Board
IMPORTANT

 The radii of the bases of two solid metallic cones of same height h are x1 & x2. If the two cones are melted together and recast into a cylinder of height h, then show that the radius of the base of the cylinder is 13x21 + x22.

MEDIUM
10th Manipur Board
IMPORTANT

    A solid metallic cylinder and another solid metallic cone have the same height h and the same radius r. If the two solids are melted together and recast into a cylinder of radius 12r, prove that the height of the new cylinder is 163 h.

MEDIUM
10th Manipur Board
IMPORTANT
Two solid metallic cuboids of dimensions 15 cm×8 cm×5 cm and 20 cm×5 cm×4 cm, are melted together and recast into solid cubes each of side 5 cm. Find the number of solid cubes so formed.
MEDIUM
10th Manipur Board
IMPORTANT
 A sphere of diameter 6 cm is dropped into a cylindrical vessel, partly filled with water. The diameter of the vessel is 12 cm. If the sphere is completely submerged, how high will the level of the water be raised?
MEDIUM
10th Manipur Board
IMPORTANT
A solid metallic cylinder of radius 14 cm and height is 21 cm is melted and recast into a number of spheres, each of radius 3.5 cm. Find the number of spheres so formed.
MEDIUM
10th Manipur Board
IMPORTANT
A spherical shell of lead, whose external diameter is 16 cm, is melted and recast into a cylinder of height 9 13 cm and diameter 16 cm. Find the internal diameter of the shell.