Question

What is the weight of the following piece if it is made of steel weighing 0.2833 pounds per cubic inch? The piece is solid. Round to the nearest hundredth. Use the r button.r1 = 18", d2 = 10", h = 13"

Answer 1

A cone is cut into two and the given piece is what we call a partial cone or a frustum.

In order to get the weight of the pice, we need to get the volume of the partial cone.

The formula for getting the volume of a partial cone is:

`V=(\pi h(R^2+Rr+r^2))/(3)`

where:

h = height of the partial cone = 13 inches

R and r = radius of the cone where R > r

In the figure, R = 18 inches while r = 5 inches (half of 10 inches diameter)

Let's replace the variables in the formula above with the given information.

`V=(\pi*13(18^2+(18)(5)+5^2))/(3)`

Then, solve.

`V=(13\pi(324+90+25))/(3)`
`V=(13\pi(439))/(3)`
`V=(5707\pi)/(3)\Rightarrow V=5,976.3564in^3`

The volume of the cone is approximately 5, 976.3564 cubic inches.

To get the weight, simply multiply the volume by the weight per cubic inch.

`Weight=5,976.3564*0.2833\approx1,693.10pounds`

The weight of the piece is approximately 1,693.10 pounds.