Volume of Cones

Front

What is the formula for the volume of a cone?

Back

V = (1/3)πr²h

Front

If a cone has a radius of 3 cm and a height of 4 cm, what is its volume?

Back

V = (1/3)π(3)²(4) = 12π cm³ ≈ 37.7 cm³

Front

What does 'r' represent in the volume formula of a cone?

Back

'r' represents the radius of the base of the cone.

Front

What does 'h' represent in the volume formula of a cone?

Back

'h' represents the height of the cone.

Front

How do you calculate the volume of a cone with a radius of 5 cm and a height of 10 cm?

Back

V = (1/3)π(5)²(10) = (1/3)π(25)(10) = (250/3)π cm³ ≈ 261.8 cm³

Front

What is the volume of a cone with a radius of 2 in and a height of 6 in?

Back

V = (1/3)π(2)²(6) = (1/3)π(4)(6) = 8π in³ ≈ 25.1 in³

Front

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

Back

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

Front

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

Back

The volume of a cone is directly proportional to its height; if height increases, volume increases.

Front

Calculate the volume of a cone with a radius of 7.5 cm and a height of 5 cm.

Back

V = (1/3)π(7.5)²(5) = 294.38 cm³

Front

What is the approximate volume of a cone with a radius of 1 m and a height of 3 m?

Back

V = (1/3)π(1)²(3) = π m³ ≈ 3.14 m³