Question

#8 iFind the volume of the composite solid. Round your answer to the nearest hundredth.3 cm3 cm10 cmThe volume is about cubic centimeters.

Answer 1

`226.19\text{ cm}^3`

Step-by-step explanation:

Here, we want to calculate the volume of the composite solid

Mathematically, that is the volume of the cylinder added to that of the cone

The volume of a cylinder is:

`V_\text{ = }\pi r^2h`

where r is the radius which is 3cm and h is the height which is (10 cm - 3cm = 7 cm)

The volume of a cone is:

`V\text{ = }(1)/(3)\pi r^2h`

where r is the base radius of the cone which is 3 cm and h is the height which is 3 cm

Substituting the values, we have it that:

`\begin{gathered} V\text{ = }\pi r^2h\text{ + }(1)/(3)(\pi r^2h) \\ \end{gathered}`

Substituting the values, we have:

`\begin{gathered} V\text{ = \lparen}\pi*3^2*7)\text{ +}((1)/(3)*\pi*3^2*3) \\ \\ V\text{ = 197.92 cm}^3\text{ +}28.27\text{ cm}^3\text{ = 226.19 cm}^3 \end{gathered}`