Firstly, split it into 2 separate shapes, the cylinder, and the hemisphere.
The formula to work out the volume of a cylinder is pi*r^2*h
Substituting the values you've been given in, that gives 3.14*4^2*7=351.68
Next, the hemisphere. The formula for the volume of a sphere is 4/3*pi*r^3
Substituting the values into this we get:
4/3*3.14*4^3=267.946....
However, the shape is a hemisphere, and that is the volume if it were a whole sphere, so we divide that number by 2 to get the volume of the hemisphere.
Dividing it by 2 gives 133.97 to 2dps.
Adding 351.68 to 133.97 gives 485.65
Therefore the volume of the shape is 485.65 in^3
