MENU

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

Question - 21 : - A cube, of side 4 cm, contains a sphere touching its sides. Find the volume of the gap in between.

Answer - 21 : - Side of cube = 4 cm
∴ Volume = (side)3 =4x4x4 = 64 cm3
Diameter of the largest sphere touching its sides = 4 cm

Question - 22 : - A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1m, then find the volume of the iron used to make the tank. (NCERT)

Answer - 22 : - Thickness of hemispherical tank = 1 cm
Inner radius (r) = 1 m = 100 cm

Question - 23 : - A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule? (NCERT)

Answer - 23 : - Diameter of a medicine spherical capsule = 3.5 mm

Question - 24 : - The diameter of the moon is approximately one fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon? (NCERT)

Answer - 24 : -

Question - 25 : - A cone and a hemisphere have equal bases and equal volumes. Find the ratio in their heights.

Answer - 25 : - Let r be the radius of cone and hemisphere and let h be the height of the cone then

Question - 26 : - A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped into the tub and thus level of water is raised by 9 cm. What is the radius of the ball?

Answer - 26 : -

Radius of cylinderical tub (r) = 16 cm
Height of water in it (h) = 30 cm

Question - 27 : - A cylinder of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the cylinder and thus the level of water is raised by 6.75 cm. Find the radius of the ball. (Use π = 22/7).

Answer - 27 : -

Radius of cylinder (r) = 12 cm
Depth of water in it (h) = 20 cm
By dropping a ball, the water level rose by 6.75 cm

Question - 28 : - A cylindrical jar of radius 6 cm contains oil. Iron spheres each of radius 1.5 cm are immersed in the oil. How many spheres are necessary to raise the level of the oil by two centimetres?

Answer - 28 : - Radius of cylinderical jar (r) = 6 cm
Level of oil in it (h) = 2 cm

Question - 29 : - A measuring jar of internal diameter 10 cm is partially filled with water. Four equal spherical balls of diameter 2 cm eacfy are dropped in it and they sink down in water completely. What will be the change in the level of water in the jar?

Answer - 29 : - Diameter of measuring jar = 10 cm

Now after swing the ball in the water of jar Letvolume of water raised, by h cm

Question - 30 : - A cone, a hemisphere and a cylinder stand on equal bases and have the same height. Show that their volumes are in the ratio 1 : 2:3.

Answer - 30 : -

∵ Bases and heights of a cones hemisphere and a cylinder are equal
Let r be the radius and h be their heights

Free - Previous Years Question Papers
Any questions? Ask us!
NodeJS Interview Questions Answers
ASP.Net Interview Questions Answers
Interview Questions Answers
×