Question 29
Choose an axial section of an equilateral cone of radius $2\,\mathrm{dm}$ and place a rectangular coordinate system on it, with origin at the base center and vertex on the positive vertical axis; each coordinate unit is $1\,\mathrm{dm}$. Calculate the vertex coordinates. Write in intercept form the equations of the lines containing the two slant sides in this axial section. Calculate the total surface area and volume of the cone. Give exact results.
Supplemental coordinate illustration (AI); perspective is not to scale.
Supplemental coordinate illustration (AI); perspective is not to scale.