Verified answer

If the radius of the surface is r,

r/3 = 5/10

r=1.5m

surface area of the top of water = pi r^2 =pi * 1.5^2

=2.25pi

ok so you are looking at a proportion type of problem..

So just picture a little cone inside of your big cone.

the little cone will be the water.

So you know 5 is related to 10 since they are both heights.

5= height of little cone

10=height of big cone

Therefore the relationship is that the height of the little cone is half of the height of the big cone.

Using that same relationship you can say that the radius of the little cone will be half the size of the radius of the big cone...

therefore:

3=radius of big cone

1.5= radius of little cone

Now, the question is asking for the surface area of the top of the water. Well the top of the water is in the shape of a circle so just find the area of the circle.

Area of Circle= πr²

At this point all you need to do is put in the value of "r" and solve. "r" is the radius of the little cone represented by the water.

therefore:

A= π(1.5²)

And TADA!!! : ) you get surface area of the top of the water = 7.068583470..........

Hope i'm right. lol

I seem to have an ambiguous interpretation of what is required. If what you mean by "surface area of the top of the water" is the area of the water surface when it is 5 meters deep, then the formula is simply

A = pi(r^2) where

r = radius of the water surface when it is 5 meters deep

By similar triangles,

r/5 = 3/10 hence

r = 1.5 m

So, if this interpretation is correct, then

A = pi(1.5)^2

A = 2.25(pi) sq meters

ANOTHER interpretation is to determine the surface area of the cone above the water level. If this is the correct interpretation, then the formula to be used is

S = pi(r)(h) + pi(r^2)

where

S = surface area

r = radius

h = slant height

The total surface area of the cone (with radius of 3 m and height of 10 m) is

So = pi(3)(10) + pi(3^2)

So = 39(pi) = 122.52 m^2

The total surface area of the cone submerged in water is

Sw = pi(1.5)(5) + pi(1.5)^2

NOTE the equivalent radius of the water surface (r = 1.5m )when the water level is 5 has been determined in the first portion of this solution.

Sw = 7.5pi + 2.25pi

Sw = 9.75pi = 30.63 m^2

Therefore, the surface area of the cone above the water level is

So - Sw = 39pi - 9.75pi = 29.25pi

So - Sw = 91.89 m^2

the surface area is wet

sometimes with a word problem - you have to root out the junk

like - as I was going to St Ives and all the cats and kittens and etc - - how many were going to St Ives?? ONE - - as I,,,

doesn't matter one whit if it's a cylinder or cone or its depth

the top area has a 3 meter radius

what is the formulae for the area of a circle - - - - ?????

All the best

I am on the way to St Ives

area of the base of the cone over the ten meter high cone is equal to area of the base in the middle of the cone over the high of meters....

let x be the area of the in the middle of a cone...

(3^2pie)/10meters=X/5meters

X=[(28.3m^2)(5meters)]/10meters

X=14.14m^2..

...i thought you said this was a math problem