Answer:
56844.9 units squared
Step-by-step explanation:
The surface area of a cone is denoted by: [tex]A=\pi r^2+\frac{1}{2} \pi r^2*l[/tex] , where r is the radius and l is the slant height. The slant height is basically the length from a point on the base circle to the top vertex of the cone.
Here, since our diameter is 50 and diameter is twice the radius, then our radius is r = 50/2 = 25.
To find the slant height, we have to use the Pythagorean Theorem:
[tex]l^2=r^2+h^2[/tex], where h is the height
[tex]l^2=25^2+50^2=625+2500=3125[/tex]
[tex]\sqrt{l^2} =\sqrt{3125}[/tex]
[tex]l=25\sqrt{5}[/tex]
Now, plug these values of r and l into the first equation above:
[tex]A=\pi r^2+\frac{1}{2} \pi r^2*l[/tex]
[tex]A=\pi *25^2+\frac{1}{2} \pi *25^2*25\sqrt{5} =625\pi +\frac{15625\sqrt{5} }{2} \pi[/tex] ≈ 56844.9 units squared
