Find the surface area and volume of cone. A = rs + r2 V = 1/3r2 h A cone's slant height (s) is 14 cm and its radius is 4.5 cm. Surface area (to the nearest tenth) = cm2 Volume (to the nearest tenth) = cm3

Answer:Surface area = [tex]261.6cm^2[/tex]Volume = [tex]281.2cm^3[/tex]Step-by-step explanation:To find the surface area of our cone, we are using the formula for the surface area of a cone: [tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex]where[tex]A[/tex] is the surface area [tex]r[/tex] is the radius [tex]h[/tex] is the height Notice that the height, radius, and slant height make a right triangle, so to find the height, [tex]h[/tex], we can use the Pythagorean theorem:[tex]s^2=r^2+h^2[/tex][tex]14^2=4.5^2+h^2[/tex][tex]196=20.25+h^2[/tex][tex]h^2=196-20.25[/tex][tex]h^2=175.75[/tex][tex]h=\sqrt{175.75}[/tex][tex]h=13.26[/tex] cmWe have all we need now to find the surface area of our cone:[tex]A=\pir(r+\sqrt{h^2+r^2} )[/tex][tex]A=\pi(4.5)(4.5+\sqrt{13.26^2+4.5^2} )[/tex][tex]A=261.6cm^2[/tex] Now, to find the volume of our cone, we are using the formula for the volume of a cone:[tex]V=\frac{\pi r^2h}{3}[/tex]where[tex]V[/tex] is the volume [tex]r[/tex] is the radius [tex]h[/tex] is the height Replacing values [tex]V=\frac{\pi (4.5^2)(13.26)}{3}[/tex][tex]V=281.2cm^3[/tex]We can conclude that the surface area of our cone is 261.6 square centimeters and its volume is 281.2 cubic centimeters.