Volume of Pyramids and Cones

Front

What is the formula for the volume of a cone?

Back

The volume V of a cone is given by the formula: V = (1/3)πr²h, where r is the radius of the base and h is the height.

Front

What is the formula for the volume of a pyramid?

Back

The volume V of a pyramid is given by the formula: V = (1/3)Bh, where B is the area of the base and h is the height.

Front

Calculate the volume of a cone with height 10cm and base radius 9cm.

Back

V = (1/3)π(9)²(10) ≈ 848 cm³.

Front

Calculate the volume of a square pyramid with side length 3cm and height 5cm.

Back

Base area B = 3² = 9 cm²; V = (1/3)(9)(5) = 15 cm³.

Front

What is the relationship between the height and volume of a pyramid?

Back

The volume of a pyramid increases with height; doubling the height doubles the volume if the base area remains constant.

Front

What is the difference between a cone and a pyramid?

Back

A cone has a circular base and tapers to a point, while a pyramid has a polygonal base and triangular faces that meet at a point.

Front

How do you find the base area of a square pyramid?

Back

The base area B of a square pyramid is found using the formula: B = side², where 'side' is the length of one side of the square base.

Front

What is the volume of a pyramid with a base area of 12 m² and height of 4 m?

Back

V = (1/3)(12)(4) = 16 m³.

Front

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

Back

If the radius is doubled, the volume increases by a factor of 4, since volume is proportional to the square of the radius.

Front

What is the volume of a cone with a base radius of 5cm and height of 12cm?

Back

V = (1/3)π(5)²(12) ≈ 100 cm³.