Answer:
We have a cylinder and two semispheres.
The volume of a cylinder is equal to:
Vc =h*pi*r^2
where h is the height, r is the radius, and pi = 3.14
We know that the diameter is d = 8.4 mm, and the radius is half of that:
r = 8.4mm/2 = 4.2mm
Then the volume of the cylinder is:
Vc = 15.2mm*3.14*(4.2mm)^2 = 841.9 mm^3
The volume of a sphere is:
Vs = (3/4)*pi*r^3
The radius of the sphere is the same as the radius of the cylinder, and for a semisphere, we have half of the volume written above,
Vss = (3/8)*3.14*(4.2mm)^2 = 87.2mm^3
and we have two of those, so the total volume is:
Vt = 841.9 mm^3 + 2*87.2mm^3 = 1016.3 mm^3
The surface area of the figure is equal to the curved surface of the cylinder plus the surface of the two semispheres.
The curved surface of the cylinder is:
Sc = 2*pi*r*h = 2*3.14*4.2mm*15.2mm = 400.9 mm^2
The surface of a sphere is:
Ss = 4*pi*r^2
and for each semisphere, we can find the surface by dividing the previous equation by two, but we have two semispheres, so we can jump a step and think the two semispheres as only one sphere.
Ss = 4*3.14*(4.2mm)^2 = 221.6mm^2
The total surface is St = 221.6mm^2 + 400.9 mm^2 = 622.5 mm^2
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