Question

Samuel cut a cone from a piece of wood shaped as a cylinder. He measured the circumference of the base of the cylinder and found that it measured 3πinches. The height of the cylindrical piece of wood was 6 inches. What is the approximate volume of Samuel's cone if it has the same base area and height as the cylinder?

Answer 1

Answer:

The approximate volume of the cone is 14 cube inches.

Step-by-step explanation:

Circumference of the base of the cylinder = 3π inches

Height of the cylindrical piece of wood = 6 inches

volume of a cone = $\frac{1}{3}$$\pi$$r^{2}$h

But,

circumference = 2πr

3π = 2πr

r = $\frac{3}{2}$

  = 1.5 inches

Radius of the base of the cylinder is 1.5 inches.

So that;

volume of cone =  $\frac{1}{3}$ x $\frac{22}{7}$ x $(\frac{3}{2}) ^{2}$ x 6

                          =  $\frac{1}{3}$ x $\frac{22}{7}$ x $\frac{9}{4}$ x 6

                          = 14.143

volume of cone = 14.143 cube inches

The approximate volume of the cone is 14 cube inches.