Answer:
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
