Question

A water tank has the shape of an inverted cone (like an ice cream cone without ice cream). 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

we know that

the surface area of the top of the water is calculated with the formula of the area of ​​a circle

$A=\pi r^{2}$

Step 1

Find the radius of the water tank in the middle of the tank

by proportion

$\frac{10}{3} =\frac{5}{x} \\ \\ 10*x=5*3\\ \\ x=\frac{15}{10} \\ \\ x=1.5m$

so

For h=5 m

the radius is equal to r=1.5 m

Step 2

Find the surface area

$A=\pi*1.5^{2}$

$A=7.07\ m^{2}$

therefore

the answer is

the surface area of the top of the water is $7.07\ m^{2}$