Volume of Cylinders, Cones, and Spheres

Front

What is the formula for the volume of a cylinder?

Back

The volume V of a cylinder is given by the formula: V = πr²h, where r is the radius and h is the height.

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 and h is the height.

Front

What is the formula for the volume of a sphere?

Back

The volume V of a sphere is given by the formula: V = (4/3)πr³, where r is the radius.

Front

Define radius in the context of a circle.

Back

The radius of a circle is the distance from the center of the circle to any point on its circumference.

Front

Define diameter in the context of a circle.

Back

The diameter of a circle is twice the length of the radius and is the distance across the circle through its center.

Front

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

Back

If the radius is doubled, the volume increases by a factor of four, since volume is proportional to the square of the radius (V = π(2r)²h = 4πr²h).

Front

What is the relationship between the radius and diameter?

Back

The diameter is twice the radius (d = 2r).

Front

Calculate the volume of a cylinder with a radius of 3 ft and a height of 5 ft.

Back

V = π(3)²(5) = 45π ≈ 141.37 ft³.

Front

Calculate the volume of a cone with a radius of 2 m and a height of 6 m.

Back

V = (1/3)π(2)²(6) = (1/3)π(4)(6) = 8π ≈ 25.13 m³.

Front

Calculate the volume of a sphere with a radius of 4 in.

Back

V = (4/3)π(4)³ = (4/3)π(64) = (256/3)π ≈ 268.08 in³.