# Right Cone

on . Posted in Solid Geometry

• Right cone (a three-dimensional figure) has a circle base with the apex alligned at 90° above the center of the base.
• 1 base

## Height of a Right Cone formula

$$\large{ h = 3\; \frac{V}{\pi \;r^2} }$$
Symbol English Metric
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{ mm }$$
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$

## Slant Height of a Right Cone formula

$$\large{ s = \sqrt {r^2+h^2} }$$
Symbol English Metric
$$\large{ s }$$ = slant height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ A }$$ = area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{ mm }$$

## Surface Area of a Right Cone formula

$$\large{ A_s = \pi\; r\; \left( r + \sqrt { h^2 + r^2 } \right) }$$
Symbol English Metric
$$\large{ A_s }$$ = surface area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \pi }$$ = Pi  $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{ mm }$$

## Volume of a Right Cone formulas

$$\large{ V = \frac {1}{3}\; \pi\; r^2 }$$

$$\large{ V = \frac {1}{3} \;b\;h }$$

Symbol English Metric
$$\large{ V }$$ = volume $$\large{ in^3 }$$ $$\large{ mm^3 }$$
$$\large{ b }$$ = base area $$\large{ in^2 }$$ $$\large{ mm^2 }$$
$$\large{ h }$$ = height $$\large{ in }$$ $$\large{ mm }$$
$$\large{ \pi }$$ = Pi  $$\large{3.141 592 653 ...}$$
$$\large{ r }$$ = radius $$\large{ in }$$ $$\large{ mm }$$

Tags: Volume Equations