Question

What is the volume of the stone that the sculptor must remove?

Answer 1

We need to find the volume of the cylinder, then the cone and subtract to get the excavated volume.

`\begin{gathered} \text{Vol of Cylinder =}\pi r^2h \\ \text{Vol of cone = }(1)/(3)\pi r^2h \\ Excavated\text{ volume = }\pi r^2h\text{ - }(1)/(3)\pi r^2h\text{ = }\pi r^2h(1-(1)/(3))=(2)/(3)\pi r^2h \end{gathered}`

We then substitute the values and find our solution.

where height, h = 8ft

radius = diameter / 2 = 3/2= 1.5 ft

`\begin{gathered} \text{Vol of Cylinder =}\pi*1.5^2\text{ }*8=56.55\text{ cu ft} \\ \text{Vol of Cone =}(1)/(3)*\pi*1.5^2\text{ }*8=18.85\text{ cu ft} \\ \text{Excavated volume =}(2)/(3)*\pi*1.5^2\text{ }*8=37.7\text{ cu ft} \end{gathered}`

V cylinder = 56.55 cu ft

V Cone = 18.85 cu ft

V remaining = 37.7 cu ft