Question

Cones A and B both have volume of 48LaTeX: \pi π cubic units, but have different dimensions. Cone A has radius (r) 6 units and height (h) 4 units. Select a possible radius (r) and height (h) for Cone B.

Answer 1

Radius = 2cm ; height = 36cm

Explanation:

Recall:

Volume of a cone (V):

1/3πr²h

r = radius ; h = height

Given that:

Cone A:

Va = 48π

ha = 4 ; ra = 6

Cone B :

Vb = 48π

hb = ? ; rb =?

Since both cones have similar volume:

Va = Vb

1/3πra²ha = 1/3πrb²hb

48π = 1/3πrb²hb

48 = 1/3rb²hb

48*3 = rb²hb

144 = rb²hb

One possible solution is :

144 = 36 * 4

Where ;

r² =4

h = 36

r = √4 ; r = 2

h = 36

Radius = 2cm ; height = 36cm