+911 Find the volume of a cone that has 12 as its base radius and a lateral surface area of 100 \pi.
+25 This cone is impossible cuz the base radius is too large for the lateral surface area.
\(h^2=625/ 9 - 1296 / 9 = (625 − 1296) / 9 = -671 / 9\)
The total volume of a cone cant be negative, so was there a typo in ur question or smthg?
unless -671/9 was the answer u were looking for...
+130037 Lateral surface area = pi * r * slant height
100 = pi * 12 * slant height
Slant height = 100 / (12 pi) = 25/ ( 3pi)
Height of the cone = sqrt [ slant height ^2 - radius^2 ] = sqrtt [ (25/(3pi))^2 - 12^2] ≈ 11.7
Volume of cone =
(1/3) h * pi * r^2 =
(1/3)(11.7)*pi (12)^2 ≈ 1764.3 u^2
