Question

find the volume of each solid if the cylinders volume is 36 cm3

Answer 1

Solution

1) The volume of a cone.

The volume of a cylinder = 36

What is the relationship between the volume of the cone and the volume of the cylinder? (Answer: The cone takes up one-third of the volume of the cylinder.)

$\begin{gathered} The\text{ volume of a cone = }\frac{1}{3}\text{ }\times\text{ Volume of a cylinder} \\ =\text{ }\frac{1}{3}\text{ }\times\text{ 36} \\ =\text{ 12cm}^3 \end{gathered}$

2) Volume of a sphere

The relation between the volume of sphere and the volume of cylinder is that the volume of the sphere is two-third of the volume of the cylinder with a height equal to the diameter of the sphere and the same radius.

$\begin{gathered} Volume\text{ = }\pi r^2h \\ Volume\text{ of a sphere = }\frac{2}{3}\pi r^2h \\ Volume\text{ of a sphere = }\frac{2}{3}\text{ }\times\text{ 36} \\ Volume\text{ of a sphere = 24 cm}^3 \end{gathered}$

Final answer