Apencil consists of a cone stacked on top of a cylinder .the diameter of the cylindrical base of the pencils is 10mm and the height of the cylinder is 70 mm while the height of the cone is 12 mm. calculate the surface area of the pencil. leave your answer in terms of pi.

790π mm^2.  

Step-by-step explanation:

The total surface area of the pencil = area of the base + lateral surface area of the cylinder + curved surface area of the cone.

The radius of the base of the pencil = 1/2 * 10 = 5 mm which is also the radius of the base of the cone.

The surface area of the  cylinder = area of the base + lateral area

= π r^2 + 2 π r h

=  25 π + 10*70 π

= 725π mm^2.

The curved surface area of the cone = r * √(h^2 + r^2)  π

= 5* √(12^2 + 5^2) π

= 65π mm^2

Total surface area = 725 π + 65 π

= 790 π mm^2.

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