How do you work out the surface area of a prism, (semicircular cross section) The Radius of the semicirlce 5.?

Question

Length of the prism 18cm.

Answer 1

Don't let this lot fob you off by working out the volume just because it's easier.
1) cut the shape into 2 semi circles(the ends),the base rectangle and the curved surface which when flattened out is a rectangle too.
Area 2 semi circles = pi x5x5=78.5
area base = 10x18 = 180
area curved bit = circumference semi circle x 18
=2xpix5/2 =15.7x18 =282.7

Add them up....541.2 sq cm.

Answer 2

Strictly speaking it isn't a prism, because the cross-section of a prism has to be a polygon, not circular.

Assuming that both ends are closed, the surface area of each end would be πr²/2, so the ends would have combined surface area of πr² = 25π

2πr gives the circumference of a circle, seeing as how this is semicircular πr gives the circumference and 18πr gives the surface area along the semicircular length which equals 18 x 5 x π = 90π

Then the base is 10 x 18 = 180

So if both ends are open the surface area is 180 + 90π

If both ends are closed the surface area is 180 + 115π

If one end is open and the other end is closed the surface area is 180 + 102.5π

Answer 3

Area of 1 semi circle, doubled.
Circumference of a circle (radius 5) halved x length of the prism
Diameter of circle x lenght of prism
So if the prism is 18cm long
Pi x 5 x 5 + 2 x 5 x 18 + Pi x 5 x 18

Answer 4

First find the area of the trapezium using the formula: 1/2(a+b) * height ((Note: a and b are the lengths of the parallel sides)) Multiply the answer you get by 2 to get the area of two sides. Let this answer equal x Next to find the area of the other sides: Add up all the sides of the trapezium and multiply by the prism's height, NOT by the height of the trapezium. Let this answer be y Then add the answer you got in section one and two and there you have it, the surface area. Total surface area = x + y

Answer 5

Total S.A = Area of 2Semi O ends + Rect. Base + Curved S.A.
={ pi x (r x r)} + {2r x 18} + {1/2 of 2 x pi x r x 18}
= 25 x pi + 180 + 90 x pi
=115 x 3.14 + 180
= 361.1 + 180
=541 cm squared (3 sig figs)

Answer 6

Well, the volume is the area of the cross section times the length. The area of a circle is pi*r sq (that's "pi r squared").
That should allow you to figure it out!

Answer 7

Half of circumference of circle = Pi x r - So vol of your shape = 18x pi x 5 = lots.

Answer 8

x=(circumference*Length)/2 ....curved area

y=diameter*length.....rectangular surface area

t=pi r sq...total area of 2 semicircles

answer=x+y+t........541.1cm sq

Answer 9

I would advise you to go with Efionrefails answere, he is a math teacher, he is so good he has a Porsche!!!

Answer 10

the cross sectional area = V/L = V/18

in this case it will be 0.5*pi*r^2