Question

find the volume of the largest right circular cone that can be cut out of a cube of edge42cm

Answer 1

Answer:

The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.

Solution:

Edge of the cube = 4.2 cm

i.e 2r = 4.2

r = 4.2/2 = 2.1 cm

h = 4.2 cm

Volume of the cone = 1/3 * pi * r^2 * h

=> 1/3 * 22/7 * 2.1 * 2.1 * 4.2

=> 19.404 cm^3

Hence, the volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is 19.404 cm^3.

Answer 2

Given:

• Edge of the cube = 42 cm

To Find:

• The volume of the cone.

Solution:

• Here we get to know that the diameter of the cone is 42 cm, from the given data.
• We can fine radius of the cone, Radius = diameter/2
• r = 42/2 = 21 cm
• The height of the cone will also be 42 cm = h
• Here the height and the diameter are the same as the edge because the cone will have the same measurements all over its surface as the edge.
• We have a formula that gives the volume of the cone, v = $\frac{1}{3}(pi)r^2h$
• v = $\frac{1}{3}(3.14)(21^2)(42) = \frac{1}{3}*3.14*441*42 = \frac{58159.08}{3} = 19.386*10^{-3} cm^3$

∴ The volume of the cone = 19.386*$10^{-3} cm^3$