December 11, 2012

Today we learned the formulas for finding the surface areas (S.A) of a:

1. Cube
2. Rectangular Prism
3. Pyramid
4. Cylinder

In order to find the surface area of a cube, use this formula:

S.A = 6 s² 

(Where "s" is the measure of 1 edge.)

That means that to find the surface area of a cube, find the area of one face of the cube first. Then square that number (multiply it by itself), and multiply it by 6 and you have your final answer.

To find the surface area of a rectangular prism, do this:

S.A = 2B + Ph

(Where "B" is the area of the base formed by multiplying its length by its width. "P" is the perimeter of the base multiplied by "h", the height of the prism. 

or.......

S.A = 2 (lw + lh + wh)

(Where "l" stands for length, "h" is height and "w" is width.)

Finding the surface area of a pyramid... :

S.A = B + ½ Ps

(Where "B" is the area of the base. "P" is the perimeter, "s" is the slant height.)

The surface area formula for a cylinder:

S.A = π r ² + 2 π rh

or......

S.A = 2 π r (r + h)

(Where "r" is radius and "h" is height.)

And lastly, for finding the surface area of an isosceles triangular prism:

S.A = 2 (bh/2) + 2 b2 h2 + B)

(Where "b" is the base of the triangle, "h" is the height of the triangle, "b2" the base of the rectangle, "h2" is the slant height of the rectangle, and "B" represents the base of the figure found by multiplying "b" by "b2"

(sorry I couldn't upload any pictures!)

Textbook Pg. 79, #17

My Question:

Some parks contain fenced gardens. Suppose that it costs $80 to build each metre of fence, including materials and labour. 

a) How much does it cost to enclose a square with an area of 120 m²? Express your answer to the nearest dollar.

b) Predict whether the total cost of enclosing two squares with an area of 60 m² each is the same as your answer for part a).

c) Test your prediction from part b) and describe your findings.

part a) The first step is trying to find the square root of 120 by using a calculator. The square root is also the same value as one side of the square garden.

√120 = 10.95

Because there are 4 sides in a square, you need to multiply 10.95 by 4.

10.95  x 4 = 43.8

Then, you need to multiply the number above by $80 to the the final answer.

43.8 x $80 = $3504

The cost of enclosing a square with an area of 120 m² is $3504

part b) Following the same procedure we used for part a), find the square root of one square with an area of 60 m²

√60 = 7.74

7.74 x 4 = 30.96

30.96 x 80 = 2476.8

And because we are finding the area of two 60 m² fenced gardens, multiply that previous answer by two.

2476.8 x 2 = $4953.6

As you can see, the results are Not The Same.

c) I predicted that the costs for the fenced gardens would not be the same because two 60 m² squares have a total of 8 sides, and a 120 m² only has four sides, therefore I knew that the area would of the 60 m² would be larger because of the greater amount of sides.

Textbook: Page 70, Question 23

23 a) Write a subtraction statement involving two negative fractions or negative mixed numbers so that the difference is -4/3 (negative four thirds).

23 b) Share your statement with a classmate.

That would be you.