Volume, Radius,Diameter

Question

What is the height and radius of a cone if the volume is 45

Answer 1

Volume = V = 45 = (1/3)hb = h(pir^2)/3

135 = pihr^2

h= 135/pir^2 = height of the cone

r^2 = 135/pih

radius = r = sqr(135/hpi)

You need more information to get a specific height and radius

the smaller the height, the larger the radius, and vice versa

Additional information needed is usually giving a value for either r or h, or giving the surface area

If r = h, then

45 = hpi(h^2)/3

pih^3 = 135

h^3 = 135/pi

h = r = cube root of 135/pi = about cube root of 43 = about 3.5

3.5 = radius = r

r^2 = 12.25

area of the cone's base = 12.25pi

h= 3.5

V = hb/3 = 3.5(12.25pi)/3 = 44.9 rounded off