Question

Find the weight of the steel rivet shown in the figure (steel weighs 0.0173 pounds per cubic centimeter)Round to the nearest tenth as needed.

Answer 1

step 1

the volume of the figure is equal to the volume of the frustums of the cone plus the volume of the cylinder

Find out the volume of the cylinder

we have

r=2.8/2=1.4 cm

h=10.7 cm

`V=\pi\cdot r^2\cdot h`

substitute given values

`\begin{gathered} V=\pi\cdot1.4^2\cdot10.7 \\ V=20.972\pi\text{ cm3} \end{gathered}`

Find out the volume of the frustum

the formula to calculate the volume is

`V=(1)/(3)\cdot\pi\cdot h\cdot\lbrack R^2+r^2+R\cdot r\rbrack`

we have

R=5.6/2=2.8 cm

r=2.8/2=1.4 cm

h=1.9 cm

substitute given values

`V=(1)/(3)\cdot\pi\cdot1.9\cdot\lbrack2.8^2+1.4^2+2.8\cdot1.4\rbrack`
`V=8.689\pi\text{ cm3}`

Adds the volumes

V=20.972pi+8.689pi

V=29.661pi cm3

Multiply by the density

29.661pi*0.0173=1.6 lb

therefore

the answer is 1.6 lb