Solving Geometry Homework

Geometry:

Geometry is the main branches of mathematics. The geometry different types of size, shape, relative position of figures, and the properties of space. Geometry is one of the oldest sciences. The word ‘Geometry’ means learn of properties of figures and shapes and the relationship between them. A system of geometry is called Euclidean geometry. A solid geometry classified to a set of problems or objects.

(Source-Wikipedia)


Solving homework 1:


To calculate the area of a cylinder given that its radius is 8 and its length or height is 6.

Solution:

The surface area of this cylinder is 2 `pi` RL+2 `pi` R2.

= 2*3.14*8*6+2*3.14*82=703.717

The surface are of a cylinder is 703.717

Solving homework 2:

To calculate the perimeter of a rectangle given that its width is 7 and its height is 6.

Solution:

The perimeter is the distance around the rectangle, or h+w+h+w or 2h+2w.

Perimeter = 2 * 6 + 2 * 7 = 26

The perimeter of rectangle is 26


Solving homework 3:


To calculate the area of a rectangle given that its width is 8 and its height is 7.

Solution:

The area enclosed by rectangle, is h × w

Area = 7 * 8 = 56

The area of a rectangle is 56

Solving homework 4:

To calculate the area of a right triangle given that its base is 10 and its height is 8.

Solution:

The area of a right triangle is 1/2bh

Area = ½ * 10 * 8 = 40

The area of a rectangle is 56

Solving homework 5:

To calculate the side of a square given that its area is 8.

Solution:

The area is the amount of space enclosed by the square is S × S or Area=S2.

Solve this equation for S to get that or S=Area1/2 Side = area ½=81/2=2.82843

The side of this square has a length of 2.82843

Solving homework 6:

To calculate the area of  rhombus whose diagonal lengths are  8 and 12.

Solution:

The area of the rhombus= 1/2  x length of the diagonal 1 x length of the diagonal 2 .

=1/2 x 8 x 12

The area of the rhombus = 48

Solving Solid Geometry

In solid geometry we study three dimensional geometry (3-D geometry).
For examples: Cube, cuboid, cylinder, cone, sphere, Pyramids, Prisms etc. Dimensions are the terms as length, width, height, thickness etc. A three dimensional figure must have length, width and height.

Cube : A three dimensional shape having equal length(a), width(a) and height (a).
Cuboid: A three dimensional shape having different length(l), width(w) and height(h).
Cylinder: A three dimensional shape having two circular faces of radius(r) at two ends and a curved surface of height(h).
Cone: A three dimensional shape having a circular face at one end and a curved surface of height(h).
Sphere: A three dimensional shape of radius r. For example: a ball.

Formulas for Solving Solid Geometry
(1) Cube :           Lateral Surface Area ( Area of four sides i.e. front, back, left, right ) = 4a2
                           Total Surface Area( Area of all six faces) = 6a2
                            Volume = a x a x a = a3
(2) Cuboid:        Lateral Surface Area ( Area of four sides i.e. front, back, left, right ) = 2h(l+w)
                            Total Surface Area( Area of all six faces) = 2( lw + wh + hl )
                             Volume = lwh
(3) Cylinder:      Curved surface area = 2Ï€rh
                            Total surface area (including two circles on both ends) = 2Ï€r(r+h)
                            Volume = 2Ï€r2h
(4) Cone :          Curved surface area = Ï€rl where l is the slant height of the cone l = `sqrt(h^2 + r^2)`
                            Total surface area (including a circles on the base) = Ï€r(r+l)
                            Volume = 1/3 Ï€r2h
(5) Sphere :      Surface area = 4Ï€r2
                            Volume = 4/3 Ï€r3

How to Solve Problems for Solid Geometry
Step 1) Make a figure of solid given in the problem.
Step 2) Write the dimensions of the solid e.g. length, width, height, radius etc.
Step 3) Apply the formula for particular solid geometry figure.
Step 4) Write the unit of the particular physical quantity e.g. square meters, cubic centimeters etc.