find the volume of cone whose height is 5 cm and its radius is 3 cm.

Question

Surface areas and volumes

Answer 1

v= (h/3)pir^2= (5/3)pi(3)^2=15pi cm^3

volume = about 15(3.14159) = about 47.124 cm^3

pi = about 3.14159

pir^2= area of the cone's base = A

cone volume = 1/3 height times area of the base

V= hA/3

the volume of a cone = 1/3 the volume of a cylinder

a cylinder's volume = hA = height times Area of its base

the usual proof of the cone's volume formula involves calculus

but you can do a practical solution. take a cylinder with same base & height as a cone,

fill the cone up with water, dump it into the cylinder, do that 3 times and you fill up the

cylinder completely, exactly Volume of a cylinder = 3 times the volume of a cone

and volume of the cone = 1/3 the volume of a cylinder

the cone volume formula works regardless whether it's a right angled cone or oblique

Surface Area of a cone with radius 3 and height 5 cm = about 83.23 cm^2

Surface Area of a Cone = pirL + pir^2 where L= slant height = sqr(h^2 +r^2) = sqr(25+9) = sqr34

= pi(rL +r^2) = pi(3sqr34+9) = about 3.14159(3sqr34+9) = 83.23 cm^2

Answer 2

V = (1/3)πr²h.

Can you substitute values and calculate?