cylinder and a cone

Question

A cylinder has the same volume as a cone if the cylinder has a radius of 8 cm and height of 9 cm why the cone has a radius of 5 cm what is I the height of the cone i i the slanting height of the cone

Answer 1

cylinder has height 9 cm and radius 8 cm

cone has radius = 5

volumes of each are equal, what is the height of the cone?

Volume of the cylinder = h(r^2) = 9(8)^2 = 9(64 = 576 cm^3

Volume of the cone = (1/3)h(r^2) = (1/3)h(5^2) = 25h/3

set them equal

25h/3 = 576

h = (3/25)576)= 1728/25

h= 6912/100 = 69.12 cm high for the cone

V = (1/3)(69.12)(5^2) = (25/3)(69.12) =25(23.04) = 576

but you want the slant height

slant height = square root of (69.12^2 + 5^2)

It's the hypotenuse of a right triangle with sides 69.12 and 5

= (69.12^2 +25)^(1/2)

= 69.30060894 cm

= about 69.3 cm = slant height