Here we have compiled:
Related Topics: More Geometry Lessons
Shape 
Volume Formula 
Surface Area Formula 
Cube 
s^{3}

6s^{2} 
Cuboid 
lwh 
2(lw
+ lh + wh) 
Prism 
area of base × height 
2 × area of base + perimeter of base × height 
Cylinder 
πr^{2}h

2πr (r
+ h) 
Hollow Cylinder 
πh(R^{2}
− r^{2}) 
2πrh
+ 2πRh + 2(πR^{2} − πr^{2}) 
Cone 

πr (r
+ s) 
Pyramid 
Any
pyramid = area of base + area of each of the lateral
faces 

Sphere 

4πr^{2} 
Hemisphere 

3πr^{2 }where r = radius 
A cube is a threedimensional figure with six matching square sides.
The figure above shows a cube. The dotted lines indicate edges hidden from your view.
If s is the length of one of its sides, then the volume of the cube is s × s × s
Volume of the cube = s^{3}
The formula for the volume of a cube is s × s × s = s^{3}, where s is the length of a side of the cube.
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 volume of the above rectangular solid would be the product of the length, width and height that is
Volume of rectangular solid = lwh
The formula for the volume of a cuboid is l × w × h = lwh, where l is the length, w is the width and h is the height of the rectangular prism. This video will give two examples of finding the volume of a rectangular prism.
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.
When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.
The volume of a right prism is given by the formula:
Volume of prism = Area of base × length
V = Al
where A is the area of the base and l is the length or height of the prism.
This video shows how to determine which is the base and the height of the triangular prism.
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 volume of a cylinder is given by the formula:V = π r^{2}h
where r = radius of cylinder and h is the height or length of cylinder.
How to find the volume of a cylinder, given that the radius is 9 and the height is 12.
Sometimes you may be required to calculate the volume of a hollow cylinder or tube.
Volume of hollow cylinder
where R is the radius of the outer surface and r
is the radius of the inner surface.
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 volume of a cone is given by the formula:
Volume of cone = Area of base × height
V = where r is the radius of the base and h is the height of the prism.
How to find the volume of a cone, given that the radius is 12 and the height is 16?
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. For example a rectangular pyramid or a triangular pyramid.
The volume of a pyramid is given by the formula:
Volume of pyramid = Area of base × height
V = where A is the area of the base and h is the height of the pyramid.
Make sure that you use the vertical height to substitute into the formula and not the slant height.
A sphere is a solid in which all the points on the round surface are equidistant from a fixed point, known as the center of the sphere. The distance from the center to the surface is the radius.
Volume of sphere = where r is the radius.
How to find the volume of a sphere? What is the volume of air in the ball?
A hemisphere is half a sphere, with one flat circular face and one bowlshaped face.
Volume of hemisphere where r is the radius
How to find the volume of a hemisphere? What is the volume of water in a bowl?