Help your students prepare for their Maths GCSE with this free volume and surface area of a sphere worksheet of 26 questions and answers
The volume of a 3D shape is the amount of space enclosed inside it. The surface area is the total area of all of the faces that make up its surface.
To calculate the volume of a sphere, we use the formula 43r3 , where r is the radius of the sphere. For example, if the radius of a sphere is 4cm, we would substitute the value 4 in for r. This can be input into a calculator and the answer rounded to a given number of decimal places or significant figures. When calculating the volume of the sphere, students can be asked to write their answer as a multiple of , requiring them to simplify the expression as far as possible, but to leave in their answer. This can sometimes result in the answer involving integers or fractions.
To calculate the surface area of a sphere, we use the formula 4r2 . For example, for a sphere with radius 4cm as above, we substitute 4 for r in the formula to calculate the surface area of the sphere. Again, students may be asked to leave their answer as a multiple of .
These skills may be applied to compound 3D shapes – for example, calculating the surface area of a hemisphere placed on top of a cylinder. In this case, we calculate the curved surface area of the hemisphere (half of the sphere), the curved surface area of the cylinder, and the area of the circle on the base. To find the total surface area, we then add the three amounts together, and finally round to a suitable number of decimal places.
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