Gr 10 Math Ch 10: The effect of multiplying a dimension by a factor of k
47 Questions
0 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What happens to the volume of a cylinder when both the radius and height are multiplied by a factor of k?

  • The volume is multiplied by $k^3$ (correct)
  • The volume remains the same
  • The volume is multiplied by $k^2$
  • The volume is multiplied by $k^4$

    • If the height of a cylinder is increased by a factor of k, how is the surface area affected?

  • The surface area is multiplied by $k$ (correct)
  • The surface area is multiplied by $k^3$
  • The surface area is multiplied by $k^2$
  • The surface area remains unchanged

    • When the radius of a cylinder is multiplied by a factor of k, how does the surface area change?

  • The surface area decreases by a factor of $k^2$
  • The surface area increases by a factor of $k$
  • The surface area remains the same
  • The surface area increases by a factor of $k^2$ (correct)

    • If the radius of a cylinder is doubled, how does the volume change?

    <p>The volume increases by a factor of 4</p> Signup and view all the answers

    What is the relationship between the change in radius and the change in volume for a cylinder?

    <p>The volume changes by the square of the factor of the radius change</p> Signup and view all the answers

    When both the radius and height of a cylinder are multiplied by k, how does the surface area change in comparison to the volume?

    <p>Surface area increases by a factor of $k^2$, volume increases by a factor of $k^3$</p> Signup and view all the answers

    What is the effect on the volume of a rectangular prism when one dimension is multiplied by a factor of 5?

    <p>The volume is multiplied by 5.</p> Signup and view all the answers

    How is the surface area affected when two dimensions of a rectangular prism are multiplied by a factor of 5?

    <p>The surface area is multiplied by 25.</p> Signup and view all the answers

    What is the formula for the volume of a rectangular prism when all dimensions are multiplied by a factor of k?

    <p>$V_k = k^3 V$</p> Signup and view all the answers

    If the original surface area of a rectangular prism is A, what will the new surface area be when all dimensions are multiplied by k?

    <p>$k^2 A$</p> Signup and view all the answers

    Which of the following statements correctly describes the change in volume and surface area when one dimension is multiplied by k?

    <p>Volume is multiplied by k, surface area by k^2.</p> Signup and view all the answers

    What volume change occurs when all three dimensions of a rectangular prism are multiplied by a factor of 5?

    <p>Volume increases to 125V.</p> Signup and view all the answers

    What happens to the surface area when both dimensions of a rectangular prism are multiplied by 2?

    <p>The surface area is multiplied by 4.</p> Signup and view all the answers

    Which of these correctly describes how the volume and surface area change when all dimensions are multiplied by a factor of k?

    <p>Volume changes by $k^3$, surface area by $k^2$.</p> Signup and view all the answers

    What is the effect on the volume of a cylinder when the radius is multiplied by 3?

    <p>Volume is multiplied by 9</p> Signup and view all the answers

    How does the surface area of a cylinder change when the height is doubled?

    <p>Surface area is doubled</p> Signup and view all the answers

    If the radius of a cylinder is tripled, what is the new surface area in relation to the original surface area?

    <p>Surface area is 9 times the original</p> Signup and view all the answers

    When the radius of a cylinder is multiplied by k, how is the effect on volume described?

    <p>Volume is increased by a factor of k²</p> Signup and view all the answers

    What happens to the volume of a cylinder when both the radius and height are multiplied by k?

    <p>Volume is multiplied by k³</p> Signup and view all the answers

    How does the surface area change if only the height of a cylinder is multiplied by k?

    <p>Surface area increases by a factor of k</p> Signup and view all the answers

    What happens to the volume of a rectangular prism when its height is multiplied by a factor of 5?

    <p>It increases by a factor of 5.</p> Signup and view all the answers

    How is the surface area affected when all three dimensions of a rectangular prism are multiplied by a factor of k?

    <p>It increases by a factor of k^2.</p> Signup and view all the answers

    If the original volume of a rectangular prism is V, what is the new volume after multiplying all dimensions by 3?

    <p>27V</p> Signup and view all the answers

    When two dimensions of a rectangular prism are multiplied by a factor of k, what is the new volume in terms of the original volume V?

    <p>k^2V</p> Signup and view all the answers

    What is the relationship between the factor applied to dimensions and the resulting volume of a rectangular prism?

    <p>The volume changes by the cube of the factor applied.</p> Signup and view all the answers

    If one dimension of a rectangular prism is doubled and the second dimension remains unchanged, how does the surface area change?

    <p>It is doubled.</p> Signup and view all the answers

    What effect does multiplying all dimensions of a cylinder by a factor of k have on its volume?

    <p>Volume increases by a factor of k^3.</p> Signup and view all the answers

    Which statement correctly describes the change in volume when only the height of a prism is multiplied by a factor of k?

    <p>The volume increases by a factor of k.</p> Signup and view all the answers

    What happens to the volume of a cylinder when the height is multiplied by a factor of k?

    <p>It is multiplied by k</p> Signup and view all the answers

    When the radius of a cylinder is increased by a factor of k, how much does the surface area increase?

    <p>Increases by a factor of k^2</p> Signup and view all the answers

    If both the radius and height of a cylinder are multiplied by k, how does the volume change?

    <p>It is multiplied by k^3</p> Signup and view all the answers

    What is the relationship between the change in radius and the surface area of a cylinder?

    <p>Surface area increases by a factor of k^2</p> Signup and view all the answers

    When the height of a cylinder is multiplied by k and the radius remains unchanged, how does the surface area change?

    <p>It is multiplied by k</p> Signup and view all the answers

    How does the volume change when both the height and radius of a cylinder are multiplied by k?

    <p>It is multiplied by k^3</p> Signup and view all the answers

    What is the volume of a rectangular prism when all dimensions are multiplied by a factor of 3 if the original volume is V?

    <p>27V</p> Signup and view all the answers

    How is the new surface area determined when one dimension of a prism is multiplied by 2?

    <p>The surface area is multiplied by 4.</p> Signup and view all the answers

    What happens to the surface area of a rectangular prism if two dimensions are multiplied by 3 and one dimension remains unchanged?

    <p>The surface area is multiplied by 12.</p> Signup and view all the answers

    If the surface area of a rectangular prism is represented as A, what will it be when one dimension is multiplied by k?

    <p>k^2A</p> Signup and view all the answers

    What will be the new volume of a rectangular prism after each dimension is increased by a factor of 4?

    <p>64V</p> Signup and view all the answers

    When both height and breadth of a prism are multiplied by k while length remains unchanged, what is the relationship of the new volume V_k to the original volume V?

    <p>V_k = k^2V</p> Signup and view all the answers

    If the volume of a cylinder is expressed as V and the height is increased by a factor of 2 while the radius is unchanged, what is the new volume in relation to the original volume?

    <p>2V</p> Signup and view all the answers

    What happens to the surface area of a rectangular prism if all dimensions are multiplied by a factor of k?

    <p>It is multiplied by k^2.</p> Signup and view all the answers

    What happens to the volume of a cylinder when the height is multiplied by a factor of k?

    <p>The volume is multiplied by k</p> Signup and view all the answers

    If the radius of a cylinder is increased by a factor of k, how does the surface area change?

    <p>The surface area is multiplied by k^2</p> Signup and view all the answers

    When both the radius and height of a cylinder are multiplied by k, how is the change in volume described?

    <p>The volume is multiplied by k^3</p> Signup and view all the answers

    What effect does multiplying only the height of a cylinder by k have on its surface area?

    <p>The surface area is multiplied by k</p> Signup and view all the answers

    If the original surface area of a cylinder is A, what will the new surface area be when the radius is doubled and the height remains unchanged?

    <p>4A</p> Signup and view all the answers

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser