the circumference of the base of 16 m high solid cone is 33 m .find the surface area of the cone

Question

Do stepwise calculation for better understanding 

Answer 1

A=∏r([r+√h^2+r^2]) is the formula to use

C=∏d

33=(3.14159)(d)

33/(3.14159)=d

d=10.5 m

r=5.25 m

A=(3.14159)(5.25)(5.25+√[16^2+5.25^2])

A=(3.14159)(5.25)(5.25+√256+27.5625)

A=(3.14159)(5.25)(5.25+√283.5625)

A=(3.14159)(5.25)(5.25+16.84)

A=(3.14159)(5.25)(22.09)

multiply the three numbers together

A=364.338 square meters

 

 

Answer 2

The lateral surface area of the cone = πr(r²+h²)^1/2 where r is the radius of the base of the cone and h is its height - you can derive this formula using calculus by taking a small sector of height dh at some specific r value r_i and integrating the surface area of the sector over the entire height of the cone. The overall surface area of the cone = lateral surface area + base area = πr(r²+h²)^1/2 +πr²

 

The circumference = 2πr = 33m, therefore r = 33/2π m,

Now plug in this value of r and h=16 m in the formula above to get your answer.