math problem help?!?

Question

A water tank has the shape of a cone. The tank is 10m high and has a radius of 3m at the top. If the water is 5m deep (in the middle), what is the surface area of the top of the water??

Answer 1

use similar triangles to figure out the radius of the water

3/10 = x/5
x=15/10
x=3/2 or 1.5

now that you have x (radius)....use area of circle formula

A = pi x r^2
A = pi (3/2)^2
A = 9/4 pi square meters

Answer 2

Because the profile of a cone is a triangle, and the vertex of the 10 m cone is the same as the 5 m cone formed by the water, we can use the principle of similar triangles. Half the height means half the radius, so a circle with a radius of 1.5 m has an area of pi*1.5^2 = 7.06858347 sq. m

Answer 3

let h = height of tank =10 m, and a = radius of base = 3 m

side of cone = sqrt(h^2+a^2) = sqrt(109) m

Now let d = 5m

The angle the cone make with the vertical can be found using

tan(q) = a/h =3/10

The radius at 5m height is then r = d*tan(q) = d*a/h

r = 5*3/10 = 3/2 = 1.5 m

so area A = pi*(1.5) m^2