Question

Find the volume of the top of the prism, volume of the bottom prism, and total volume of figure.

Answer 1

Volume of the top of the prism: 460 cm^3

Volume of the bottom of the prism: 1 768 cm^3

Total volume of the figure: 2 228 cm^3

Step-by-step explanation:

Volume of the top of the prism:

. Since it is a prism from trapezoid

. . Volume = Area of the trapezium base * heights between trapezium ends

`\begin{gathered} Area\text{ of a trapezium base}=\frac{top\text{ base+bottom base}}{2}*height \\ ...\text{ =}(6+17)/(2)*(22-17) \\ ...=(23)/(2)*5 \\ Area\text{ = 57.5 cm}^2 \end{gathered}`
`Volume=57.5*8=460\text{ }cm^3`

Volume of the bottom prism:

. Since the price has a rectangular base:

Volume = Area of one base * height between reactangular bases

Area of one base :

`17*13=221\text{ }cm^2`

Volume:

`221*8=1\text{ }768\text{ }cm^3`

Total volume of the figure:

Volume of the top + Volume of the bottom = Total volume

`221+1\text{ }768=2\text{ }228\text{ }cm^3`

NB:

To find any volume of a given prism, start with finding the area of one base, then multiply that area by the height (in other words the sides that link the two bases)