Answer:
864π cm²
Step-by-step explanation:
The formula for the surface area of a cone is given as:
[tex]SA = \pi r \ell + \pi r^2[/tex]
r is the radius of the circular base of the cone. So, in this case, r = 18 cm.
[tex]\ell[/tex] is the slant height of the cone. This is the distance from the apex of the cone to any point on the circumference of the base, measured along the lateral surface.
The slant height [tex]\ell[/tex] is also represented by the hypotenuse of a right triangle formed by the radius r and the height h. Therefore, to calculate the slant height given the radius r and the height h, we can use the Pythagorean theorem:
[tex]\ell^2=r^2+h^2[/tex]
Given that r = 18 cm and h = 24 cm, then the slant height [tex]\ell[/tex] of the cone is:
[tex]\ell^2=18^2+24^2\\\\\ell^2=324+576\\\\\ell^2=900\\\\\ell=\sqrt{900}\\\\\ell=30\; \sf cm[/tex]
Now that we have the radius r = 18 cm and the slant height [tex]\ell[/tex] = 30 cm, we can substitute these values into the given surface area of a cone formula and solve for SA:
[tex]SA = \pi \cdot 18 \cdot 30 + \pi \cdot 18^2\\\\SA = 540\pi + 324\pi \\\\SA=864\pi[/tex]
Therefore, the surface area of the given cone in terms of π is:
[tex]\LARGE\boxed{\boxed{864\pi \sf \; cm^2}}[/tex]
