Geometry Answers

Find the equation (formula) of a circle with radius r and center C(h,k) and if the Center of a circle is at (3,-1) and a point on the circle is (-2,1) find the formula of the circle.

Find the equation (formula) of a sphere with radius r and center C(h, k, l) and show that x² + y² + z² - 6x + 2y + 8z - 4 = 0 is an equation of a sphere. Also, find its center and radius.

In an isosceles trapezoid the 5- cm altitude drawn from the endpoint of the shorter base to

the larger base divides the larger base in segments of 10 cm and 25 cm long. Compute for

the area of the trapezoid.

The narrowness and wideness of a curve is determined by the standard deviation of the distribution. *

how far from the base pf a 24 unit wall should a 26-unit ladder be leaning so that it reaches the top most part of the wall

Find the volume of a cylindrical water tank whose radius is 25 inches and whose height is 120 inches. Use π = 3. 14

There are other geometries. One such is spherical geometry.

What can you say about the sum of the interior angles of a triangle in spherical geometry?

This question is concerning the completion of the square by using plane geometry

The area of a

The area of a rectangle of sides x and y is : xy

Consider the expression : x

2 + 10x

Such can be considered as the sum of two areas viz square x

2 and a rectangle 10x

Now do the following (sketch essential)

Divide the rectangle into two equal areas viz 5x and 5x

Next to the square place the two rectangles with the side x in common. One to the RHS and the other below.

You will now have a ’nearly complete’ square

a) What is the length of each side of the ’missing square’ in your diagram

b) If you add the area of the missing square to make a big square, what is the area of the complete (big) square

c) By using the areas from your sketch, find the expressions ? and ?? in the following:

x

2 + 10x + (?)2 = (??)2

Calculate the circumference of a circle with a diameter of 1.2mm

All of the previous questions used what we know as Euclidean geometry.

There are other geometries. One such is spherical geometry.

What can you say about the sum of the interior angles of a triangle in spherical geometry?

This question is concerning the completion of the square by using plane geometry

The area of a square of length x is : x

2

The area of a rectangle of sides x and y is : xy

Consider the expression : x

2 + 10x

Such can be considered as the sum of two areas viz square x

2 and a rectangle 10x

Now do the following (sketch essential)

Divide the rectangle into two equal areas viz 5x and 5x

Next to the square place the two rectangles with the side x in common. One to the RHS and the other below.

You will now have a ’nearly complete’ square

a) What is the length of each side of the ’missing square’ in your diagram

b) If you add the area of the missing square to make a big square, what is the area of the complete (big) square

c) By using the areas from your sketch, find the expressions ? and ?? in the following:

x

2 + 10x + (?)2 = (??)