# Sphere

on . Posted in Solid Geometry

• Sphere (a three-dimensional figure) has all points equally spaces from a given point of a three dimensional solid.
• Lune of a sphere is the space occupied by a wedge from the center of the sphere to the surface of the sphere.
• Sector of a sphere is the space occupied by a portion of the sphere with the vertex at the center and conical boundary.
• Segment and zone of a sphere is the space occupied by a portion of the sphere cut by two parallel planes.
• Sperical cap is the space occupied by a portion of the sphere cut by a plane.

### Circumference of a Sphere formula

$$C = 2 \; \pi \; r$$
Symbol English Metric
$$C$$ = circumference $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$
$$d$$ = diameter $$in$$ $$mm$$

### Diameter of a Sphere formula

$$d = 2\;r$$
Symbol English Metric
$$d$$ = diameter $$in$$ $$mm$$
$$r$$ = radius $$in$$ $$mm$$

### RADIUS of a sphere formula

$$r = \sqrt{ S \;/\; 4 \; \pi }$$

$$r = \sqrt{ ( 3 \;/\; 4 ) \; ( V \;/\; \pi ) }$$

Symbol English Metric
$$r$$ = radius $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$S$$ = surface area $$in^2$$ $$mm^2$$
$$V$$ = volume $$in^3$$ $$mm^3$$

### Surface Area of a sphere formula

$$S = 4\; \pi \;r^2$$
Symbol English Metric
$$S$$ = surface area $$in^2$$ $$mm^2$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

### Volume of a sphere formula

$$V = \frac{4}{3} \; \pi \;r^3$$

$$V = \pi \; d^3 \;/\; 6$$

Symbol English Metric
$$V$$ = volume $$in^3$$ $$mm^3$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

### Surface Area of a sphere Cap formula

$$S = 2 \; \pi \; r \; h$$
Symbol English Metric
$$S$$ = surface area $$in^2$$ $$mm^2$$
$$h$$ = height $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

### VOLUME of a sphere Cap formula

$$V = \frac {1}{3} \; \pi\;h^2 \left( 3 r - h \right)$$

$$V = \frac {1}{6} \; \pi\;h \left( 3 r_1{^2} + h^2 \right)$$

Symbol English Metric
$$V$$ = volume $$in^3$$ $$mm^3$$
$$h$$ = height $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$
$$r_1$$ = radius $$in$$ $$mm$$

### Surface Area of a sphere Segment formula

$$S = 2 \; \pi \; r \; h$$
Symbol English Metric
$$S$$ = surface area $$in^2$$ $$mm^2$$
$$h$$ = height $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

### VOLUME of a sphere Segment formula

$$V = \frac {1}{6} \; \pi\;h \left( 3 r_1{^2} + 3 r_2{^2} + h^2 \right)$$
Symbol English Metric
$$V$$ = volume $$in^3$$ $$mm^3$$
$$h$$ = height $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$
$$r_1$$ = radius $$in$$ $$mm$$
$$r_2$$ = radius $$in$$ $$mm$$

### Surface Area of a sphere WEDGE formula

$$S = \frac{ \theta }{ 360 } \; 4 \; \pi \; r^2$$
Symbol English Metric
$$S$$ = surface area $$in^2$$ $$mm^2$$
$$\theta$$ = angle $$deg$$ $$rad$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

### Volume of a sphere WEDGE formula

$$V = \frac{ \theta }{ 2 \; \pi } \; \frac{ 4 }{ 3 } \; \pi \; r^2$$
Symbol English Metric
$$V$$ = volume $$in^3$$ $$mm^3$$
$$\theta$$ = angle $$deg$$ $$rad$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$

### VOLUME of a sphere SECTOR formula

$$V = \frac {2}{3}\; \pi \; r^2\;h$$
Symbol English Metric
$$V$$ = volume $$in^3$$ $$mm^3$$
$$h$$ = height $$in$$ $$mm$$
$$\pi$$ = Pi $$3.141 592 653 ...$$
$$r$$ = radius $$in$$ $$mm$$
$$r_1$$ = radius $$in$$ $$mm$$