Gr 10 Math Ch 10: Right Pyramids, Cones and Spheres
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Questions and Answers

What is the formula for calculating the surface area of a right cone?

  • $ ext{Area of base} + ext{Area of walls}$ (correct)
  • $ ext{Area of base} + 2 ext{Area of sides}$
  • $4 rac{1}{3} imes ext{Area of base}$
  • $ rac{1}{3} imes ext{Area of base} imes ext{Height}$

    • Which of the following descriptions accurately defines a right pyramid?

  • A pyramid with a circular base and apex not perpendicular to the base
  • A pyramid that has all sides perpendicular to its base
  • A pyramid with a polygon as its base and apex perpendicular to the base's center (correct)
  • A geometric shape with balanced triangular faces and no apex

    • What is the surface area formula for a square pyramid?

  • $b(b + 2h_s)$ (correct)
  • $4 imes rac{1}{2} b h_s$
  • $2b + 2h_s$
  • $b^2 + rac{1}{2} b h_s$

    • What factor is used to find the volume of a triangular pyramid?

    <p>$ rac{1}{3} imes ext{Area of the base} imes H$</p> Signup and view all the answers

    How do you calculate the volume of a right cone?

    <p>$ rac{1}{3} imes ext{Area of base} imes H$</p> Signup and view all the answers

    Which formula correctly represents the surface area of a sphere?

    <p>$4 ext{π}r^2$</p> Signup and view all the answers

    What does the apex of a pyramid refer to?

    <p>The point where all faces converge</p> Signup and view all the answers

    Which of the following characteristics is exclusive to spheres?

    <p>All points on the surface are equidistant from the center</p> Signup and view all the answers

    What is the volume formula for a square pyramid?

    <p>$\frac{1}{3} b^2 H$</p> Signup and view all the answers

    How does the surface area of a right cone relate to its circular base?

    <p>It equals the area of the base plus the area of the circular wall.</p> Signup and view all the answers

    For a triangular pyramid, which components are included in the surface area formula?

    <p>Base area and area of the three side triangles.</p> Signup and view all the answers

    What distinguishes the apex of a right pyramid from that of a cone?

    <p>In a right pyramid, the apex is above the center of any polygon base.</p> Signup and view all the answers

    What is the correct surface area formula for a sphere?

    <p>$4\pi r^2$</p> Signup and view all the answers

    Which of the following statements about volume is true for a right cone?

    <p>The volume is equal to the area of the base times the height.</p> Signup and view all the answers

    Which component does NOT contribute to the surface area of a square pyramid?

    <p>Volume of the pyramid.</p> Signup and view all the answers

    When comparing the surfaces of a square pyramid and a triangular pyramid, what differs in their surface area calculations?

    <p>The number of triangular faces influencing the surface area.</p> Signup and view all the answers

    What is the primary difference between a right pyramid and a right cone in terms of base shape?

    <p>A right pyramid has a polygonal base, while a right cone has a circular base.</p> Signup and view all the answers

    In the surface area formula for a square pyramid, what does the variable $h_s$ represent?

    <p>The height of the triangular side.</p> Signup and view all the answers

    What is the surface area of a sphere in terms of its radius $r$?

    <p>4πr^2</p> Signup and view all the answers

    Which of the following correctly expresses the volume of a triangular pyramid?

    <p>$ rac{1}{3} imes rac{1}{2} b h imes H$</p> Signup and view all the answers

    How is the volume of a sphere expressed in terms of its radius $r$?

    <p>$ rac{4}{3} imes ext{π} imes r^3$</p> Signup and view all the answers

    Which of the following statements about the surface area of a right cone is incorrect?

    <p>The surface area consists of only the lateral area.</p> Signup and view all the answers

    In which situation does the formula for the volume of a square pyramid apply?

    <p>When the base is a square.</p> Signup and view all the answers

    What is the correct volume formula for a triangular pyramid?

    <p>$\frac{1}{3} \left(\frac{1}{2} b h\right) H$</p> Signup and view all the answers

    In the surface area formula for a right cone, what does the term $\pi r h$ represent?

    <p>The lateral area of the cone</p> Signup and view all the answers

    Which component is included in the surface area calculation of a square pyramid?

    <p>The area of the triangular sides</p> Signup and view all the answers

    For a sphere, what does the formula $4\pi r^2$ represent?

    <p>The surface area of the sphere</p> Signup and view all the answers

    How does the volume of a square pyramid relate to its base area and height?

    <p>It's one third of the product of the base area and height.</p> Signup and view all the answers

    What defines a right pyramid as opposed to a regular pyramid?

    <p>The apex must be directly above the center of the base</p> Signup and view all the answers

    Which of the following is not a characteristic of spheres?

    <p>They appear different from varying angles</p> Signup and view all the answers

    What does the variable $h_s$ represent in the surface area formula for a square pyramid?

    <p>The height of the triangular side</p> Signup and view all the answers

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