Answer:
[tex]m=8.6464\ Kg[/tex]
Step-by-step explanation:
step 1
Find the volume of the trapezoidal prism
The volume of the prism is equal to
[tex]V=BL[/tex]
where
B is the area of the trapezoidal face
L is the length of the prism
Find the area of the base B
we know that
The area of a trapezoid is equal to
[tex]B=\frac{1}{2}[6+10](4)=32\ cm^2[/tex]
we have
[tex]L=14\ cm[/tex]
substitute
[tex]V=32(14)=448\ cm^3[/tex]
step 2
Find the mass
Remember that
The density is equal to divide the mass by the volume
so
[tex]D=\frac{m}{V}[/tex]
we have
[tex]D=19.3\ g/cm^3[/tex]
[tex]V=448\ cm^3[/tex]
substitute
[tex]19.3=\frac{m}{448}[/tex]
solve for the mass
[tex]m=19.3(448)=8,646.4\ g[/tex]
Convert to Kg
Remember that
[tex]1\ Kg=1,000\ g[/tex]
therefore
[tex]m=8.6464\ Kg[/tex]
