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RD Chapter 21 Surface Areas and Volume of a Sphere Ex 21.2 Solutions

Question - 11 : - A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of the cylinder.

Answer - 11 : - Radius of a sphere (r) = 4 cm

Question - 12 : - A vessel in the form of a hemispherical bowl is full of water. The contents are emptied into a cylinder. The internal radii of the bowl and cylinder are respectively 6 cm and 4 cm. Find the height of water in the cylinder.

Answer - 12 : - Radius of hemispherical bowl (r) = 6 cm

Question - 13 : - The diameter of a copper sphere is 18 cm. The sphere is melted and is drawn into a long wire of uniform circular cross-section. If the length of the wire is 108 m, find its diameter.

Answer - 13 : - Diameter of a copper sphere = 18 cm

Question - 14 : - The diameter of a sphere is 6 cm. It is melted and drawn into a wire of diameter 0.2 cm. Find the length of the wire.

Answer - 14 : - Diameter of a sphere = 6 cm

Question - 15 : - The radius of the internal and external surfaces of ahollow spherical shell are 3 cm and 5 cm respectively. If it is melted andrecast into a solid cylinder of height 2 cm. Find the diameter ofthe cylinder.

Answer - 15 : - Internal radius of the hollow spherical shell (r) = 3cm
and external radius (R) = 5 cm

Question - 16 : - A hemisphere of lead of radius 7 cm is cast into aright circular cone of height 49 cm. Find the radius of the base.

Answer - 16 : - Radius of hemisphere (r) = 7 cm

Question - 17 : - A hollow sphere of internal and external radius 2 cm and 4 cm respectively is melted into a cone of base radius 4 cm. Find the height and slant height of the cone.

Answer - 17 : -

Internal radius of a hollow sphere (r) = 2 cm
and external radius (R) = 4 cm
∴ Volume of the metal used

Question - 18 : - A metallic sphere of radius 10.5 cm is melted and thus recast into small cones each of radius 3.5 cm and height 3 cm. Find how many cones are obtained.

Answer - 18 : - Radius of a metallic sphere (R) = 10.5 cm

Question - 19 : - A cone and a hemisphere have equal bases and equal volumes. Find the ratio Of their heights.

Answer - 19 : - Let r be the radius and h be the height of the cone, hemisphere

Question - 20 : - The largest sphere is carved out of a cube of side 10.5 cm. Find the volume of the sphere.

Answer - 20 : - By carving a largest sphere out of the cube, the diameter of the sphere = 10.5

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