What is the first simplified equation for volume

Cube:

cube

Volume = a3 = a × a × a

Cylinder:

cylinder

Volume = π × r2 × h

π = 3.14

h is the height

r is the radius

Rectangular solid or cuboid:

Rectangular prism

Volume = l × w × h

l is the length

w is the width

h is the height

Sphere:

Sphere

Volume = (4 × π × r3)/3

π = 3.14

r is the radius

Cone:

Cone

Volume = (π × r2 × h)/3

pi = 3.14

r is the radius

h is the height

Pyramid:

Pyramid

Volume = (B × h)/3

B is the area of the base

h is the height

A little less common volume formulas

Ellipsoid:

Ellipsoid

Volume = (4 × π × a × b × c)/3

Use π = 3.14

Hollow cylinder:

Hollow cylinder

Volume = π × R2 × h - π × r2 × h

Volume = π × h ( R2 - r2)

Use π = 3.14.

How to use the volume formulas to calculate the volume.

Cube

The length of a side = a = 2 cm

Volume = (2 cm) = 2 cm × 2 cm × 2 cm = 8 cm3

Cylinder

The height is 8 inches and the radius is 2 inches.

Volume = π × r2 × h = 3.14 × (2 in)2 × 8 in = 3.14 × 4 × 8 in3

Volume = 3.14 × 32 in3 = 100.48 in3  

Rectangular solid or cuboid  

The length is 6 cm, the width is 3 cm and the height is 5 cm.

Volume = l × w  × h =  6 × 3 × 5 = 90 cm3

Sphere  

The radius = r = 20  

Volume = (4 × π × r3)/3 = [4 × 3.14 × (20)3]/3 = 3.14 × (20)3 × 4

Volume = 3.14 × 8000 × 4 = 3.14 × 32000 = 100480

Cone  

The radius is equal to 3 and the height is equal to 4.

Volume = (π × r2 × h)/3 = [3.14 × (3)2× 4]/3 = 3.14 × 9 × 4

Volume = 3.14 × 36 = 113.04

Pyramid

A pyramid has a height of 6 feet. If the base of a pyramid is a square with a length of 2 feet, find the volume.

Volume = (B × h)/3

B = area of base  = 2 ft × 2 ft = 4 ft2

Volume = (4 × 6)/3 ft3 = 24/3 ft3 = 8 ft3

Ellipsoid

The radii of an ellipsoid are 1 cm, 2, cm, and 3 cm.

Volume = (4 × π × a × b × c)/3 = (4 × 3.14 × 1 × 2 × 3)/3

Volume = ( 3.14 × 4 × 6)/3 = ( 3.14 × 24)/3 = 81.64/3 = 25.12 cm3  

Hollow cylinder

The outer radius is 8, the internal radius is 6, and the height is 10.

Volume = π × h ( R2 - r2) = π × 10 ( 82 - 62) = π × 10 ( 64 - 36)

Volume = π × 10(28) = π × 280 = 879.2

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)