In these lessons, we shall be looking at
Related Topics: More Geometry Lessons
Shape 
Surface Area Formula 
Volume Formula 
Cube 
6s^{2} 
s^{3} 
Cuboid 
2(lw
+ lh + wh) 
lwh 
Prism 
2 × area of base + perimeter of base × height 
area of base × height 
Cylinder 
2πr (r
+ h) 
πr^{2}h 
Hollow Cylinder 
2πrh
+ 2πRh + 2(πR^{2} − πr^{2}) 
πh(R^{2}
− r^{2}) 
Cone 
πr (r
+ s) 

Pyramid 
Any
pyramid = area of base + area of each of the lateral
faces 

Sphere 
4πr^{2} 

Hemisphere 
3πr^{2} 

Explanations for the volume formulas.
A cube is a threedimensional figure with six equal square sides. The figure below shows a cube. The dotted lines indicate edges hidden from your view.
If s is the length of one of its sides, then the area of each side of a cube is s^{2}. Since a cube has six squareshape sides, its total surface area is 6 times s^{2}.
Surface area of a cube = 6s^{2}
Worksheets to calculate volume and surface area of cubes.
More examples about the volume of cubes.
More examples about the surface area of cubes.
This video shows how to find the surface area of a cube using the formula
Total surface area = 6s^{2} where s is the length of a side
A rectangular solid is also called a rectangular prism or a cuboid. In a rectangular solid, the length, width and height may be of different lengths.
The surface area of the above cuboid would be the
sum of the area of all the surfaces.
Total area of top and bottom surfaces is lw + lw =
2lw
Total area of front and back surfaces is lh + lh
= 2lh
Total area of the two side surfaces is wh + wh
= 2wh
Surface area of rectangular solid = 2lw + 2lh + 2wh = 2(lw + lh + wh)
Worksheets to calculate the
volume and surface area of rectangular prisms.
More
examples about the volume of cuboids.
More
examples about the surface area of cuboids.
How to find the surface area of a rectangular prism or cuboid?
A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. The other faces are in the shape of rectangles. They are called lateral faces.A prism is named after the shape of its base.
The surface area of a prism is the sum of the area of all its external faces.
We can also use the formula
Surface area of prism = 2 × area of base + perimeter of base × height
Worksheets to calculate volume of prisms and
pyramids.
More
examples about the volume of prisms.
More
examples about the surface area of prisms.
How to find the surface area of a triangular prism by adding the area of the external faces?
This video shows how to find the surface area of a triangular prism using the formula SA = ab+(s1+s2+s3)h.
A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the centre of the sphere. The distance from the centre to the surface is the radius.
Surface area of a sphere with radius r = 4 πr^{2}
Worksheets to calculate the volume of spheres.
Worksheets to calculate the surface area of spheres.
More
examples about the volume of spheres.
More
examples about the surface area of spheres.
How to find the surface area of a sphere?
A cylinder is a solid that has two parallel faces which are congruent circles. These faces form the bases of the cylinder. The cylinder has one curved surface. The height of the cylinder is the perpendicular distance between the two bases.
The net of a solid cylinder consists of 2 circles and one rectangle. The curved surface opens up to form a rectangle.
Surface area = 2 × area of circle + area of rectangle
Surface Area = 2πr^{2} + 2πrh = 2πr (r + h)
Worksheets to calculate
volume of cylinders.
Worksheets to calculate
surface area of cylinders.
Worksheets to calculate
volume and surface area of cylinders.
Worksheets to calculate
surface area of cylinders and pipes.
More
examples about the volume of cylinders.
More
examples about the surface area of cylinders.
How to find the surface area of a cylinder? This video will show how to obtain the total surface of a cylinder by looking at the net of the cylinder.
Sometimes you may be required to calculate the total surface area of a hollow cylinder or tube.
Total surface area of hollow cylinder
= area of internal curved surface + area of external curved surface + area of the two rings
= 2πrh + 2πRh + 2(πR^{2} − πr^{2})
A cone is a solid with a circular base. It has a curved surface which tapers (i.e. decreases in size) to a vertex at the top. The height of the cone is the perpendicular distance from the base to the vertex.
The net of a solid cone consists of a small circle and a sector of a larger circle. The arc of the sector has the same length as the circumference of the smaller circle.
Surface area of cone = Area of sector + area of circle
= πrs + πr^{2} = πr(r + s)
Worksheets to calculate the
volume of cones.
More
examples about the volume of cones.
More
examples about the surface area of cones.
How to find the surface area of a cone?
A pyramid is a solid with a polygonal base and several triangular lateral faces. The lateral faces meet at a common vertex. The height of the pyramid is the perpendicular distance from the base to the vertex. The pyramid is named after the shape of its base.
We can find the surface area of any pyramid by adding up the areas of its lateral faces and its base.
Surface area of any pyramid = area of base + area of each of the lateral faces
If the pyramid is a regular pyramid, we can use the formula for
the surface area of a regular pyramid.
where p is the perimeter of the base and s is the slant height.Surface area of regular pyramid = area of base + ps
If the pyramid is a square pyramid, we can use the formula for the surface area of a square pyramid.
Surface area of square pyramid = b^{2} + 2bs
where b is the length of the base and s is
the slant height.
Worksheets to calculate the
volume of square pyramids.
Worksheets to calculate the volume of prisms
and pyramids.
More examples about the volume of pyramids.
More
examples about the surface area of pyramids.
How to find the surface area of regular pyramid?