Chapter 9

• What is the formula for the volume of a pyramid?


  Volume of pyramid = $\frac{1}{3} \times \text{area of base} \times \text{perpendicular height}$
• What is the formula for the volume of a cone?


  Volume of a cone = $\frac{1}{3}\pi r^2 h$
• How do you calculate the area of the curved surface of a cone?


  Area of a curved surface = $\pi r l$
• What is the formula for the surface area of a cone?


  Surface Area of a cone = $\pi r l +$$\pi r^2$
• What is the formula for the volume of a sphere?


  Volume of a sphere = $\frac{4}{3}\pi r^3$
• What is the formula for the surface area of a sphere?


  Surface area of a sphere = $4\pi r^2$
• What is the formula for the volume of a hemisphere?


  Volume of a hemisphere = $\frac{4}{3}\pi r^3 +$$2$
• What is the formula for the surface area of a hemisphere?


  Surface area of a hemisphere = $\frac{4\pi r^2}{2} +$$\pi r^2$
• How is the gradient defined in mathematics?


  Gradient = change in y over change in x
• What does the equation $y =$$2x$ represent in terms of gradient?


  The equation shows a gradient of 2
• What is the area of a sector formula?


  Area of sector = $\frac{\theta}{360} \times \pi r^2$
• How do you calculate the arc length of a sector?


  Arc length = $\frac{\theta}{360} \times 2\pi r$
• What is the definition of area in geometry?


  Area is the number of square units in a 2-Dimension
• What is the formula for the area of a parallelogram?


  Area of a parallelogram = base x perpendicular height
• What is the formula for the area of a trapezium?


  Area of a trapezium = $\frac{a+b}{2} \times h$
• What is the formula for the volume of a prism?


  Volume of Prism = area of cross-section x length
• What is the formula for the volume of a cylinder?


  Volume of cylinder = $\pi r^2 h$
• What is the formula for the surface area of a cylinder?


  Surface area of cylinder = $2\pi r^2 +$$2\pi rh$
• What are the key formulas for volume and surface area of pyramids and cones?

  • Volume of pyramid = $\frac{1}{3} \times \text{area of base} \times \text{perpendicular height}$
  • Volume of cone = $\frac{1}{3}\pi r^2 h$
  • Area of curved surface = $\pi r l$
  • Surface Area of cone = $\pi r l +$$\pi r^2$
• What are the key formulas for volume and surface area of spheres and hemispheres?

  • Volume of sphere = $\frac{4}{3}\pi r^3$
  • Surface area of sphere = $4\pi r^2$
  • Volume of hemisphere = $\frac{4}{3}\pi r^3 +$$2$
  • Surface area of hemisphere = $\frac{4\pi r^2}{2} +$$\pi r^2$
• What are the formulas for area and surface area of various shapes?

  • Area of sector = $\frac{\theta}{360} \times \pi r^2$
  • Arc length = $\frac{\theta}{360} \times 2\pi r$
  • Area of parallelogram = base x perpendicular height
  • Area of trapezium = $\frac{a+b}{2} \times h$
• What are the formulas for volume and surface area of prisms and cylinders?

  • Volume of Prism = area of cross-section x length
  • Volume of cylinder = $\pi r^2 h$
  • Surface area of cylinder = $2\pi r^2 +$$2\pi rh$
• Triangle area formula


  A = (b × h) / 2, where A is the area, b is the base, and h is the height
• Rectangle area formula


  A = l × w, where A is the area, l is the length, and w is the width
• Parallelogram area formula


  A = b × h, where A is the area, b is the base, and h is the height
• Trapezium area formula


  A = (h1 + h2) × (b / 2), where A is the area, h1 and h2 are the heights, and b is the base
• Circle area formula


  A = πr^2, where A is the area and r is the radius
• Sector area formula


  A = (θ/360) × πr^2, where A is the area, θ is the angle in degrees, and r is the radius
• Segment area formula


  A = (θ/360) × πr^2 - A of a sector, where A is the area, θ is the angle in degrees, and r is the radius
• Cone volume formula


  V = (1/3) × πr^2h, where V is the volume, r is the radius, and h is the height
• Cone surface area formula


  SA = πr(l + r), where SA is the surface area, r is the radius, and l is the slant height
• Cylinder volume formula


  V = πr^2h, where V is the volume, r is the radius, and h is the height
• Cylinder surface area formula


  SA = 2 × πr(h + r), where SA is the surface area, r is the radius, and h is the height
• Sphere volume formula


  V = (4/3) × πr^3, where V is the volume and r is the radius
• Sphere surface area formula


  SA = 4 × πr^2, where SA is the surface area and r is the radius
• Cuboid volume formula


  V = l × w × h, where V is the volume, l is the length, w is the width, and h is the height
• Cuboid surface area formula


  SA = 2 × (lw + lh + wh), where SA is the surface area, l is the length, w is the width, and h is the height