1.4.a1bd Slide 1 Volume of a Rectangular Prism The formula is: V =(l)(w)(h) Substituting in these values we get V = (2 in)(7 in)(3 in) Teaching Concept #1 Suppose we have a rectangular prism with a length of two inches, width of seven inches, and height of three inches, what will the volume be? Solving yields V = 42 in 3

1.4.a1bd Slide 2 Surface Area of a Triangular Prism We want to find the surface area of a triangular prism of base 8, height 3, and length 7. Teaching Concept #2 Therefore, substituting in our values we end up with SA = 2(1/2)(8)(3) + 3(7)(5) SA = 129 The formula is: SA = 2(1/2)(b)(h) + 3(l)(w). Substituting we get SA = 2(1/2)(8)(3) + 3(7)(w) To figure out the width, we must use the Pythagorean Theorem to find the length of the width of our rectangular face. This ends up being w 2 = , which can easily be solved to get w = 5.

1.4.a1bd Slide 3 Volume of a Cylinder Find the volume of a cylinder with a height of 8cm and a radius of 2cm. The formula for the volume of a Cylinder is: V = π(r 2 )(h) Teaching Concept #3 Substituting our values yields: V = π(22)(8) V = 32π cm 3

1.4.a1bd Slide 4 Surface Area of a Cylinder Teaching Concept #4 Plugging in our values yields: SA = 2π(22) + 2π(2)(8) SA = 40π cm 2 The formula for the surface area of a cylinder is: SA = 2π(r 2 ) + 2πrh. Find the surface area of the cylinder with a height of 8cm and a radius of 2cm.

1.4.a1bd Slide 5 Exponential Growth Compounded annually You put $1000 in the bank. The bank will give you 5% interest every year. How much money will you have after 10 years? The formula for compound interest is: y = P(1 + r) t Teaching Concept #5 Substituting our values we get: y = 1,000( ) 10 y = $1,628.89

1.4.a1bd Slide 6 Exponential Growth Compounded semiannually The new formula is: y = P[1 + (r/n)] nt Therefore, plugging in our values this time will be: y = 1,000[1 + (0.05/20] (2)(10) The bank will give you 2.5% interest, but compound it semiannually. In other words, it will calculate the interest every six months. The formula is now a bit different, how does the money you make change if you still invest $1,000 for 10 years? Teaching Concept #6 Hence, y = $1,638.61, which is more than before!

1.4.a1bd Slide 7 Example #1 Suppose you have a cylindrical container of soda that your soda company produces. The container has a radius of (3/4) of an inch and a height of 4 inches. How many cubic inches of soda can you fit into a twelve pack of soda? Application #1 Step 1: The formula for the volume of a cylinder is π(r 2 )h. Step 2: Plugging in our values will create π((3/4) 2 )(4) = (9π/4) cubic inches. Step 3: Multiply by the number of cans: (12 )(9π/4) = 27π cubic inches.

1.4.a1bd Slide 8 Concrete Example #1 Example #2 You are given a cylindrical bucket to carry water from the river to the local hospital in a tribal village in the middle of Tribalia. You need to transfer 100,000 cubic inches of water to the village. If the radius of your circle is one foot and your height is two feet, how many trips will you have to take? Step 1: Write down the formula for a cylinder. Step 2: Substitute in the values to get: V = π(1 2 )(2) = 2π = 6.28 cubic feet. Step 3: Convert that value to cubic inches, noticing that there are 1,728 cubic inches to one cubic feet. Therefore (1,728)(6.28) = 10, cubic inches exist in our barrell. Step 4: Now, dividing the amount we want will give us the number of trips we must take. i.e. 100,000/10, = Therefore, it will take 10 trips.

1.4.a1bd Slide 9 Demonstration #1 What is the surface area of a 5 x 6 x 7 rectangular prism? Step-by-Step #1 First of all, realize that the formula for the surface area of a rectangular prism is: SA = 2(l)(w) + 2(w)(h) + 2(l)(h) Then, we simply plug in our values and solve: SA = 2(5)(6) + 2(6)(7) + 2(5)(7) = 214.

1.4.a1bd Slide 10 Demonstration #2 I have a cylinder with a radius of 3 and a height of 5. What is the surface area of that cylinder? Step-by-Step #2 First off, write down the formula for the surface area of a cylinder: SA = 2π(r 2 ) + 2πrh. Now, plug in our values: 2π(3 2 ) + 2π(3)(5). Solving yields: 48π units squared.

1.4.a1bd Slide 11 Demonstration #3 Let’s say that a house costs $150,000. Somehow, you have been evading the government after your 15,000 dollar down payment and they haven’t realized you have defaulted on every mortgage payment. What will you owe after 5 years, if the interest rate is 5% and the interest is compounded semiannually? Step-by-Step #3 Again, the first thing we should do is to write down our formula: y = P[1 + (r/n)] nt Now, we can plug in our known information: y = 135,00[1 + (0.05/2)] (2)(5) Solving tells us that y = $172,