SA 6 s 2 SA 6 4 2 SA 616 SA 96 The surface area of the cube is 96 cm 2 b The

Sa 6 s 2 sa 6 4 2 sa 616 sa 96 the surface area of

This preview shows page 24 - 28 out of 32 pages.

SA = 6 s 2 SA = 6( 4 ) 2 SA = 6(16) SA = 96 The surface area of the cube is 96 cm 2 . b) The diagram models the Pythagorean relationship. The relationship between the areas of the squares on the sides of a right triangle is represented by the formula c 2 = a 2 + b 2 , where a and b are the legs of the triangle and c is the hypotenuse. c 2 = a 2 + b 2 c 2 = 5 2 + 12 2 c 2 = 25 + 144 c 2 = 169 The area of the square attached to the hypotenuse is 169 cm 2 . 3.4 Using Exponents to Solve Problems MHR 115
Image of page 24
Use a formula to solve each problem. a) A right triangle has two shorter sides that measure 8 cm and 15 cm. What is the area of a square attached to the hypotenuse of the right triangle? b) What is the surface area of a cube with an edge length of 3 m? Show You Know c) Method 1: Calculate in Stages The formula for the area of a square is A = s 2 , where s is the side length of the square. A = s 2 A = 20 2 A = 400 The area of the square is 400 cm 2 . The formula for the area of a circle is A = π r 2 , where r is the radius of the circle. The diameter of the circle is 20 cm. Therefore, the radius is 10 cm. A = π r 2 A = π ( 10 ) 2 A = π (100) A 314 … The area of the circle is approximately 314 cm 2 . Calculate the area of the shaded region. You can subtract the area of the circle from the area of the square. 400 - 314 = 86 The area of the shaded region is about 86 cm 2 . Method 2: Evaluate One Expression Calculate the area of the shaded region. You can subtract the area of the circle from the area of the square. A = s 2 - π r 2 A = 20 2 - π ( 10 ) 2 A = 400 - π (100) A 400 - 314 A 86 The area of the shaded region is about 86 cm 2 . 15 cm 8 cm 3 m 116 MHR Chapter 3
Image of page 25
Example 2: Develop a Formula to Solve a Problem A dish holds 100 bacteria. It is known that the bacteria double in number every hour. How many bacteria will be present after each number of hours? a) 1 b) 5 c) n Solution a) After 1 h, the bacteria population doubles. 100 × 2 = 200 After 1 h, there will be 200 bacteria. b) In a period of 5 h, the bacteria population doubles five times. 100 × 2 × 2 × 2 × 2 × 2 = 100(2 5 ) = 100(32) = 3200 After 5 h, there will be 3200 bacteria. c) After n hours, the bacteria population doubles n times. Number of bacteria = 100(2 n ) After n hours, there will be 100(2 n ) bacteria. A type of bacterium is known to triple every hour. There are 50 bacteria to start with. How many will there be after each number of hours? a) 3 b) 5 c) t Show You Know Use a Variable Strategies Key Ideas Powers are found in many formulas. When repeated multiplication is present in a formula, it is represented as a power. The use of powers keeps the formula as short as possible. Many patterns that involve repeated multiplication can be modelled with expressions that contain powers. s s s Volume of a cube = s 3 3.4 Using Exponents to Solve Problems MHR 117
Image of page 26
Check Your Understanding Communicate the Ideas 1. The surface area, SA , of a sphere can be calculated using the formula SA = 4 × π × r × r , where r is the radius. Rewrite the formula using powers and no multiplication signs. Identify the coefficient, variable, and exponent in your formula.
Image of page 27
Image of page 28

You've reached the end of your free preview.

Want to read all 32 pages?

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern

Stuck? We have tutors online 24/7 who can help you get unstuck.
A+ icon
Ask Expert Tutors You can ask You can ask You can ask (will expire )
Answers in as fast as 15 minutes