Help your students prepare for their Maths GCSE with this free volume and surface area of cones worksheet of 34 questions and answers
A cone is a 3d shape. It has a circular base and one continuous face which tapers to a point, often referred to as the apex. The apex of a right circular cone is directly above the centre of the circular base.
To find the volume of a cone we use the formula: V = one third✖πr2✖h where r is the radius of the base of the cone, and h is the perpendicular height of the cone.
For example, the volume of the cone with radius r=3cm and height h=10cm is V=30π.
To find the total surface area of a cone, we find the area of each face and add them together. The area of the base of the cone is found using the formula: A = π✖r2 . The curved surface area of a cone is found using the formula: A = πrl, where r is the radius of the base and l is the slant height of the cone. These areas are then added to give the total surface area of the cone. Note, if you flatten the curved surface area of the cone, you will get a major sector of a circle with radius l (the slant height of the cone).
If we do not know the slant height l of the cone, we can use Pythagoras’ Theorem where the base of the right-angled triangle is the radius of the base of the cone, and the perpendicular height of the right-angled triangle is the height of the cone.
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