Volume of Pyramids and Cones Explained

What is the volume formula for a pyramid?

• Volume = 1/3 * Base Area * Height

• Volume = Base Area * Height

• Volume = 1/2 * Base Area * Height

• Volume = 2 * Base Area * Height

What geometric method is used to find the height of a cone when given the slant height and radius?

• Integration

• Trigonometric ratios

• Pythagorean theorem

• Algebraic manipulation

What is the base area of a cone with a radius of 9 feet?

• 9π square feet

• 243π square feet

• 81π square feet

• 27π square feet

How do you calculate the height 'H' in an oblique cone using the tangent function?

• H = Adjacent * tan(Angle)

• H = Opposite / tan(Angle)

• H = Opposite * tan(Angle)

• H = Hypotenuse / tan(Angle)

What is the volume of an oblique cone with a base radius of 2.5 cm and height approximately 30.023 cm?

• 98.25 cm³

• 589.5 cm³

• 295.75 cm³

• 196.5 cm³

What trigonometric function is used to find the apothem of a pentagonal base in a pyramid?

• Cosecant

• Tangent

• Cosine

• Sine

What is the formula to find the side length of a pentagon when the radius and apothem are known?

• Side length = Radius * cos(Angle)

• Side length = Radius * sin(Angle)

• Side length = 2 * Radius * tan(Angle / 2)

• Side length = 2 * Radius * sin(Angle / 2)

What is the volume of a pyramid with a pentagonal base, side length 7.265 m, apothem 5 m, and height 12 m?

• 1453 m³

• 181.625 m³

• 726.5 m³

• 363.25 m³

How is the height of a pyramid calculated using the Pythagorean theorem?

• Height = √(Slant Height² - Base Length²)

• Height = Slant Height + Base Length

• Height = Slant Height² - Base Length²

• Height = √(Slant Height² + Base Length²)

What is the role of trigonometry in finding dimensions for volume calculations?

• It is not used in volume calculations.

• It is used to calculate area directly.

• It is used to find missing side lengths and heights.

• It is used to find angles only.