Find the area of the canvas required to make the tent?

Question

If the cicus tent is made by a cylinder of diameter 24m and height 11m and it is surmounted by a cone ,if the vertexof the tent is 16m above the ground

Answer 1

Draw a picture of a cone inside a cylinder with the vertex of the cone coming out of the top of the cylinder. We have to find the surface area of the cylinder without either of the bases.

To do this, we find the circumference of the base and multiply it by the height.

2(pi)rh=SA
(pi)dh=SA
(24)(11)(pi)=SA
Our surface area of the bottom portion of the tent is 264pi.

To find the area of the cone at the top, we need to know the formula for the lateral surface area of a cone (no base).

LA=Pi(r)(sqrt[r^2+h^2])
r=radius
h=height

We know the height because all that we must do is subtract the height of the cylinder from the height of the cone. 16-11=5
h=5
r=12 because the diameter of the cylinder is 24 and half of 24 is 12.

LA=Pi(r)(sqrt[r^2+h^2])
LA=Pi(12)(sqrt(12^2+5^2))
LA=Pi(12)(13)
LA=156pi

Now, add our 2 answers together.

156pi+264pi=420pi

So, it will take us 420pi sq. meters to make the tent.

I hope that this helps.

Answer 2

ok so you have a
cylinder with height 11.
cone with height 5. ( since tent is 16 meter height )

surface cylinder is height times length = 11 + pi*24

( if you unroll the cylinder its a rectangle whose height is 11 and width is pi * diameter circle. )

surface of the cone = pi * r * sqrt( r^2 + h^2 )
here r = 24/2 ( diameter / 2 )
and h = 5

so

surface cone = pi * 12 * sqrt( 144 + 25) = pi * 12 * 13

addding up the two I leave to you.

Answer 3

Hello..
to find the area of Tent = area of cyclinder + area of cone ..
area of cyclinder = pi r^ h ...
given r = 24/2 =12 ,
and h = 11m
so area of cylindrical portion is = 2 pi r h = 2 pi (12 x 11) = 264pi

area of conical part = pi (r ) l

radius of conical part = radius of cylindrical part .= 12m
Height (H) = total height of tent - height of cylindrical portion
= ( 16 - 11 )m = 5m .

Slant height ( l ^2 ) = ( h^2 + r^2 ) (PYTHOGOREAN THM)
= ( 5^2 + 12^2 )
l^2 = ( 25 + 144)
l = sqrt ( 169 ) =13
area of conical part is = pi (12)( 13)
= 156pi

so total area is = 264pi + 156 pi = 420 pi
= 420 (3.14) = 1318.8 sq m

Answer 4

1320 sq m

ans curved surface area of the cylinder and cone
i.e 2(22/7)rh+(22/7)rl
where r = radius = 24/2 =12
h=11
l=sqrroot(5^2 + 12^2)
l is slant height of cone