You have a cone with surface area of 628.32 m². In order to find the volume of the cone you use the following formula:
V= 1/3 π r² h
r: radius of the base of the cone = 15m/2 = 7.5m
h: heigth of the cone
Then, you have to calculate first the height of the cone. To do that, you use the information about the surface area. You use the following formula:
S = πr² + πrl
l: diagonal of the cone
Then, you have to find l, and then you can calculate hYou solve for l from the surface area formula:
l = (S - πr²)/πr = (628.32 - π(7.5)²)/(π(7.5))
l = 19.16
To calculate the heigth of the cone you use the Pythagoras theorem, just as follow:
h = √(l²-r²) = √((19.16)²-(7.5)²) = 17.63m
Next, you can replace the values of h and r into the formula for the Volume:
V= 1/3 π r² h = (1/3)π (7.5m)²(17.63m) = 1038.5m³
Hence, the volume of the given cone is 1038.49 m3