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Form 2 Questions and Answers on Volume of Solids

In this session, Form 2 Questions on Volume of Solids will be covered.

Lessons (32)

• 1.    Calculate the volume of a sphere whose radius is: (a) 4.8 cm (b) 21 cm
  1m 9s

• 2.    A solid metal cylinder is 60 cm long and 18 cm in diameter. Determine the number of solid spheres of diameter 8 cm that can be moulded from the cylinder.
  1m 57s

• 3.    The internal and external radii of a spherical shell are 8 cm and 9 cm respectively. Calculate the volume of the material of the shell to the nearest #cm^3#.
  1m 20s

• 4.    A cylindrical tank of radius 0.6 m contains water to a depth of 1 m. A solid metal sphere of radius 0.5 m is placed in it. Calculate the rise of the water level in centimetres.
  2m 6s

• 5.    The volume of water in a measuring cylinder is 25. 2 #cm^3#. After a solid metal sphere is immersed into it, the measuring cylinder reads 29.4 #cm^3#. Calculate the radius of the sphere.
  1m 59s

• 6.    The mass of 1 #cm^3# of lead is 11.4 g. Calculate the mass of a lead sphere whose radius is 15 cm.
  1m 34s

• 7.    If 1 #cm^3# of copper metal has a mass of 8.88 g, calculate the mass of a quarter sphere of copper whose radius is 24 cm.
  1m 37s

• 8.    A spherical container which is 30 cm in diameter is #3/4# full of water. The water is emptied into a cylindrical container of diameter 12 cm. Find the depth of the water in the cylindrical container.
  1m 58s

• 9.    A solid copper sphere of diameter 36 cm is to be moulded from a copper wire 0.8 mm in diameter. Find the length of copper wire required to make the sphere?
  2m 2s

• 10.    Find the volume of each of the following pyramids: (a) Triangular base, sides 5 cm, 12 cm and 13 cm, height 24 cm. (b) Square base, side 6 cm, height 10 cm. (c) Rectangular base, 8 cm by 10 cm, height 12 cm.
  3m 43s

• 11.    Find the volume of each of the following right pyramids: (a) Rectangular base, 18 cm by 24 cm, slant edge 39 cm. (b) Square base, side 8 cm slant edge 8 cm. (c) Triangular base, sides 10 cm, 12 cm and 4 cm, height 24 cm.
  8m 42s

• 12.    (a) The volume of a pyramid is 120#cm^3#. Calculate its height and the surface area if the base is a square of side 6 cm. (b) Find the height of a pyramid with base area 24 #cm^2# and volume 96#cm^3#.
  4m 2s

• 13.    Calculate the height and the length of the slant edge of a right pyramid whose base is a square of side 5 cm and volume 125#cm^3#.
  3m 22s

• 14.    The volume of a right pyramid of height 16 cm on a square base is 192 #cm^3#. Calculate the length of the side of the base.
  1m 21s

• 15.    VABCD is a right pyramid with a square base ABCD. Calculate its volume if the height is 12 cm and the slant edge is 16 cm.
  3m 14s

• 16.    The figure below is a net of a pyramid with a square base of side 32 cm. The other four faces are isosceles triangles whose equal sides are 34 cm each. Calculate the volume of the pyramid.
  3m 6s

• 17.    Calculate the volume of a pyramid of height 14 cm and a square base of side 24.
  0m 40s

• 18.    A cone has a base radius of 9.44 cm and a volume of 113.6 #cm^3#. Calculate the height of the cone.
  1m 15s

• 19.    Find the volume of the following cones: (a) Slant height 17 cm, height 7 cm. (b) Base radius 9 cm, height 24 cm.
  2m 37s

• 20.    Find the volume of each of the following cones: (a) Base area 18 #cm^2#, height 6 cm. (b) Slant height 15 cm. height 9 cm. (c) Base perimeter 16 cm, height 10 cm.
  3m 11s

• 21.    Calculate the total surface area and volume of a frustum of a pyramid whose ends are squares of 10 cm and 12 cm and the height between the two ends is 4 cm.
  6m 10s

• 22.    A toy consists of a conical top and a cylindrical base. The diameter of the base is 5 cm and the height of the cylindrical part is 4 cm. If the total height of the toy is 9 cm, calculate: (a) its total surface area. (b) its total volume.
  3m 43s

• 23.    A frustum is cut from a cone whose radius is r cm and height h cm. If the height of the frustum is t centimetres, express the volume of the frustum as a fraction of the volume of the cone.
  4m 46s

• 24.    The figure below shows a triangle in which AB = 18 cm, BC = 6 cm, BD = 7 cm and DE is parallel to BC. If the triangle is rotated about AB, calculate: (a) the surface area of the cone formed. (b) the volume of the cone.
  3m 11s

• 25.    A path is 300 m long and 1.8 m wide. Find the volume of gravel needed to cover it to a depth of 5 cm.
  1m 19s

• 26.    Calculate the volume of a metal tube whose internal diameter is 70 mm and thickness 7 mm, if it is 15 cm long.
  3m 41s

• 27.    A water tank of height 2.5 m has a uniform cross-section in the shape of a rectangle with semi-circular ends as shown in the figure below. The inside length of the tank is 7 m and its width 4 m. Calculate the: (a) area of the base. (b) volume of the tank. (c) capacity of the tank in litres.
  3m 4s

• 28.    A steel metal bar has the shape of a regular hexagon of side 2 cm, and it is 20 cm long. Calculate: (a) the cross-section area of the metal bar. (b) the volume of the metal bar. (c) the mass in kilograms of the metal bar if 1 #m^3# of steel weighs 7 800 kg.
  6m 14s

• 29.    A concrete tower on which a water tank is to be placed has a uniform octagonal cross-section of side 3 m. If its height is 24 m, find the volume of concrete used to make it.
  4m 13s

• 30.    A metal rod of 20 m length has an isosceles triangular base, where the equal side are 12 cm each. If the included angle in the base is 40°, calculate: (a) the area of the cross-section. (b) the volume of the metal rod. (c) the mass of the metal rod, if it is made of copper, whose density is 9 000 kg/#m^3#.
  2m 39s

• 31.    The cross-section of a container is in the shape of a trapezium. The two parallel sides of the container are 3.6 m and 2.1 m long, while the perpendicular height between them is 2.4 m. If its length is 6 m, find the volume of the container.
  1m 45s

• 32.    The figure below represents a swimming pool. Calculate: (a) the volume of the pool in cubic metres. (b) the capacity of the pool in litres.
  2m 18s