Exam Lessons Mathematics

Surface Area and Volume of a Sphere, Hemisphere and Composite Shape


A solid in geometry is a shape with length, width, and height. It is not a flat shape. Some of the common solids are cuboid, cube, cylinder, cone, square based pyramids, sphere etc.

Below are sketches of common solids listed above.


  1. Calculate the total surface area of a solid hemisphere of radius 7.7cm. (Take π = 22/7)
  2. Calculate the volume and surface area of a hemisphere of diameter 9cm.

General Evaluation

  1. A hemisphere bowl has an external radius 0f 18cm and is made of wood 3cm thick. Calculate the volume of wood in the bowl.
  2. A measuring cylinder of radius 3cm contains water to a  height  of  49cm.If  this  water  is poured into similar cylinder of radius 7cm, what will be the height of the water column
  3. From a cylindrical object of diameter 70cm and height 84cm, a right solid cone having its base as one of the circular ends of the cylinder and height 84cm is removed. Calculate
    1. the volume of the remaining solid object expressing your answer in the form of a x 10n
    1. the surface area of the remaining solid object.

Reading Assignment:

New General Mathematics, chapter 3, pages 16 -19.

Essential Mathematics for SS3, by AJS Oluwasanmi, chapter 7, pages 88 -90

Weekend Assignment

  1. What is the surface area of a sphere, radius 1cm to 3s.f.?
  2. Find the volume of a hemisphere of diameter 4cm (a) 16.8cm2(b) 16.8cm3                (c ) 15.8cm3      (d) 15.8cm2
  3. The volume of a sphere is 4190cm3. What is its radius?     (a) 15cm            (b)14cm (c) 12cm       (d) 10cm.
  4. What is the diameter of a sphere of surface area 804cm2? (a) 18cm (b) 17cm (c) 19cm (d) 16cm
  5. What is the volume of a hemisphere of diameter 9cm?(a) 190cm3(b) 191cm3(c ) 192cm3 (d) 193cm3


  1. A sphere has a volume of 1000cm3(a) Calculate its radius correct to 3.s.f.

(b) Find the surface area of the sphere. A hemisphere bowl has an external radius of 24cm and is made of wood 3cm thick calculate the volume of wood in the bowl.

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