Surface area of prisms and cylinders

12. 785.375 in^2

13. 20.666 in.

14. 9cm

Step-by-step explanation:

12. The surface area of a cylinder is given by the surface area of each end plus the surface area of the side:

Surface area = 2 π r^2 + 2 π r h

we know that r = diameter / 2 = 10in/2 = 5in

height = 20 in

Then:

Surface area = 2 π r^2 + 2 π r h =  2 π (5in)^2 + 2 π (5in) (20in) = 785.375 in^2

13. A rectangular prism has 2 ends and 4 sides. Opposite sides have the same area. The surface area is the sum of the areas of all six sides. Then we have:

Area=2b+ph  

where:  

b= area of a base  = 6 in^2

p= perimeter of a base  = 18 in

h= height of the prism

Area = 384 sqrt units

Solving for "h" we have:

Area=2b+ph -> h = (area - 2b)/p = 20.666 in

Then: Area= 20.666 in.

14. We know that the surface area of a cylinder is:

Surface area = 2 π r^2 + 2 π r h

Solving for "h" we have:

h = (Surface area - 2 π r^2)/ 2 π r

Where r = 4cm

Surface area = 326.73 cm^2

h = (Surface area-2πr^2)/2πr=(326.73 cm^2-2π(4cm)^2)/2π(4cm) = 9cm

h =9cm

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