Answer:
The surface area without the base is 753.6 square inches
The surface area with the base is 1,205.75 square inches
Step-by-step explanation:
The lateral surface area of a right cone using the slant height is [tex]\pi r l[/tex] where r is the radius and l is the slant height. We know the slant height is 20 inches. To find the radius, use the circumference given and solve for r.
[tex]C = 2\pi r\\\\24\pi = 2\pi r\\\\\frac{24\pi}{2\pi} = r \\12=r[/tex]
Now find the lateral surface area [tex]\pi (20)(12) = 753.6[/tex]
This is the surface area without the base. Add the lateral surface area to the area of the base [tex]A=\pi r^2\\A =\pi (12)^2\\A = 452.16[/tex]
The total surface area is 452.16 + 753.6 = 1, 205.76
