Volume And Surface Area ALPHA Maths Module : Pipeng Free Online Software

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Pipeng Free Online Software : Volume And Surface Area ALPHA Maths Module

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Pipeng : Maths Geometry : Volume And Surface Area ALPHA Maths Homework Module

Volume And Surface Area ALPHA Maths Module

Description : Maths Geometry : Volume And Surface Area

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ALPHA : Geometry : Cone 01 : Surface Area And Volume Of A Cone : ALPHA Maths Homework Exercise

Description : Surface area and volume of a cone.

Discussion : A cone is a circular pyamid. See figure Basic 3D Geometry : Sphere And Cone Shapes

The homework exercise has 4 questions.

surface area A

volume V

slope length s from A

height h from V

The equations are :

A = π r(r + s) = π d / 2 (d / 2 + s)

V = 1/3 π r² h = 1/12 π d² h

s = A / (π r) - r = 2 A / (π d) - d / 2

h = 3 V / (π r²) = 12 V / (π d²)

where

r = radius

d = diameter = 2 r

s = slant length

h = height

A = surface area

V = volume

ALPHA : Geometry : Cylinder 01 : Surface Area And Volume Of A Cylinder : ALPHA Maths Homework Exercise

Description : Surface area and volume of a cylinder.

Discussion : A cylinder has a circular cross section of radius r and diameter d. See figure Basic 3D Geometry : Cylinder Shapes

The homework exercise has 4 questions.

surface area A

volume V

height h from A

radius r from V

The equations are :

A = 2 π r (r + h) = π d (d / 2 + h)

V = π h r² = π h d² / 4

h = A / ( 2 π r) - r = √(A / (π d) - d / 2)

where

r = radius

d = diameter = 2 r

h = height

A = surface area

V = volume

ALPHA : Geometry : Cylinder 02 : Surface Area And Volume Of A Tube : ALPHA Maths Homework Exercise

Description : Surface area and volume of a tube.

Discussion : A tube is a hollow cylinder. See figure Basic 3D Geometry : Cylinder Shapes

The homework exercise has 4 questions.

surface area A

volume V

height h from A

height h from V

The equations are :

A = π / 2 (d² - id²) + π (d + id) h

V = π / 4 (d² - id²) h

h = (A - π / 2 (d² - id²)) / (π (d + id))

h = 4 V / (π (d² - id²))

where

id = inside diameter

d = diameter

h = height

A = surface area

V = volume

ALPHA : Geometry : Cylinder 03 : Surface Area And Volume Of A Half Cylinder : ALPHA Maths Homework Exercise

Description : Surface area and volume of a half cylinder.

Discussion : A half cylinder is a cylinder cut in half along its axis, the extension of a semi circle. See figure Basic 3D Geometry : Cylinder Shapes

The homework exercise has 4 questions.

surface area A

volume V

height h from A

height h from V

The equations are :

A = π / 4 d² + (π / 2 + 1) d h

V = π / 8 d² h

h = (A - π d² / 4) / ((π / 2 + 1) d)

h = 8 V / (π d²)

where

d = diameter

h = height

A = surface area

V = volume

ALPHA : Geometry : Cylinder 04 : Surface Area And Volume Of A General Cylindrical Section : ALPHA Maths Homework Exercise

Description : Surface area and volume of a general cylindrical section.

Discussion : A general cylinder has cross section x and perimeter p. See figure Basic 3D Geometry : Cylinder Shapes

The homework exercise has 4 questions.

surface area A

volume V

cross section area x from A

height h from V

The equations are :

A = 2 x + h p

V = h x

x = (A - h p) / 2

h = V / x

where

x = cross section area of cylinder

p = cross section perimeter of cylinder

h = height

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 01 : Surface Area And Volume Of A Cube : ALPHA Maths Homework Exercise

Description : Surface area and volume of a cube.

Discussion : All the sides of a cube are equal. See figure Basic 3D Geometry : Cuboid Shapes

The homework exercise has 4 questions.

surface area A

volume V

length l from A

length l from V

The equations are :

A = 6 l²

V = l³

l = √(A / 6)

l = ³√(V)

where

l = length of sides

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 02 : Surface Area And Volume Of A Rectangular Cuboid : ALPHA Maths Homework Exercise

ALPHA : Geometry : Polyhedron 03 : Surface Area And Volume Of A Square Pyramid : ALPHA Maths Homework Exercise

Description : Surface area and volume of a square pyramid.

Discussion : The pyramid has a square base and four equal triangular sides. The slope length is the perpendicular length of the sides. See figure Basic 3D Geometry : Pyramid Shapes

The homework exercise has 4 questions.

surface area A

volume V

length l from A

length l from V

The equations are :

A = l² + 2 l s

V = 1/3 l² h

l = -s + √(s² + A)

l = √(3 V / h)

where

l = length of base

s = slope length

h = height

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 04 : Surface Area And Volume Of An Equilateral Triangle Based Pyramid : ALPHA Maths Homework Exercise

Description : Surface area and volume of an equilateral triangle based pyramid.

Discussion : The pyramid has an equilateral triangle base, and three equal triangle sides. See figure Basic 3D Geometry : Pyramid Shapes

The homework exercise has 4 questions.

surface area A

volume V

slope length s from A

height h from V

The equations are :

A = l / 2 * (w + 3s)

V = 1/6 l w h

s = (2 A / l - w) / 3

h = 6 V / (l w)

where

l = length of base

w = perpendicular width of base

s = slope length

h = height

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 05 : Surface Area And Volume Of A Regular Triangle Pyramid (Four Equilateral Triangles) : ALPHA Maths Homework Exercise

Description : Surface area and volume of a regular triangle pyramid.

Discussion : A regular triangular pyramid has four equal sides, all equilateral triangles. See figure Basic 3D Geometry : Pyramid Shapes

The homework exercise has 4 questions.

surface area A

volume V

width w from A

height h from V

The equations are :

A = 2 l w

V = 1/6 l w h

w = A / (2 l)

h = 6 V / (l w)

where

l = length of base

w = perpendicular width of triangles

h = height

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 06 : Surface Area And Volume Of A Trapezoid Prism : ALPHA Maths Homework Exercise

Description : Surface area and volume of a trapezoid prism.

Discussion : A trapezoid prism has a trapezoid cross section. A trapezoid has two parallel sides. See figure Basic 3D Geometry : Prism Shapes

The homework exercise has 4 questions.

surface area A

volume V

width w from A

height h from V

The equations are :

A = w (b + d) + h (a + b + c + d)

V = w h (b + d) / 2

w = (A - (a + b + c + d) h) / (b + d)

h = 2 V / (w (b + d))

where

a b c d = sides of trapezoid

w = perpendicular width of trapezoid

h = height

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 07 : Surface Area And Volume Of A Triangle Prism : ALPHA Maths Homework Exercise

Description : Surface area and volume of a triangle prism.

Discussion : The prism has a triangular cross section. See figure Basic 3D Geometry : Prism Shapes

The homework exercise has 4 questions.

surface area A

volume V

width w from A

height h from V

The equations are :

A = b w + (a + b + c) h

V = b h w / 2

w = (A - (a + b + c) h) / b

h = 2 V / (h w)

where

a b c = sides of triangle

w = perpendicular width of triangle

h = height

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 08 : Surface Area And Volume Of A Parallelogram Prism : ALPHA Maths Homework Exercise

Description : Surface area and volume of a parallelogram prism.

Discussion : The prism has a parallelogram cross section. See figure Basic 3D Geometry : Prism Shapes

The homework exercise has 4 questions.

surface area A

volume V

width w from A

height h from V

The equations are :

A = 2 b w + 2 (a + b) h

V = b h w

w = (A - 2(a + b) h) / (2 b)

h = V / (b w)

where

a b = sides of parallelogram

w = perpendicular width of parallelogram

h = height

A = surface area

V = volume

ALPHA : Geometry : Polyhedron 09 : Surface Area And Volume Of A General Prism : ALPHA Maths Homework Exercise

Description : Surface area and volume of a general prism.

Discussion : A general prism has a cross section area x, and a cross section perimeter p. See figure Basic 3D Geometry : Prism Shapes

The homework exercise has 4 questions.

surface area A

volume V

cross section area x from A

height h from V

The equations are :

A = 2 x + h p

V = h x

x = (A - h p) / 2

h = V / x

where

x = cross section area of prism

p = cross section perimeter of prism

h = height

A = surface area

V = volume

ALPHA : Geometry : Sphere 01 : Surface Area And Volume Of A Sphere : ALPHA Maths Homework Exercise

Description : Surface area and volume of a sphere.

Discussion : A sphere has constant radius and diameter. See figure Basic 3D Geometry : Sphere And Cone Shapes

The homework exercise has 4 questions.

surface area A

volume V

radius r from A

diameter d from V

The equations are :

A = 4 π r² = π d²

V = 4/3 π r³ = π / 6 d³

r = √(A / (4 π))

d = ³√(8 V / π )

where

r = radius

d = diameter = 2 r

A = surface area

V = volume

ALPHA : Geometry : Sphere 02 : Volume Of An Spheroid : ALPHA Maths Homework Exercise

Description : Volume of an spheroid.

Discussion : For a sheroid two of the three axis are equal. The axis a and b are half axis, corresponding to radius. See figure Basic 3D Geometry : Sphere And Cone Shapes

The homework exercise has 3 questions.

volume V

axis a from V

axix b from V

The equations are :

V = 4/3 π a b²

a = 3 V / (4 π b²)

b = √(3 V / (4 π a))

where

a b = major and minor half axis

V = volume

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