Volume of cylinders, cones and spheres

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 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 sphere?

Back

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

Front

If a cone has a radius of 3 inches and a height of 9 inches, what is its volume?

Back

V = (1/3)π(3)²(9) = 27π in³, approximately 84.82 in³.

Front

A cylinder has a radius of 5 cm and a height of 10 cm. What is its volume?

Back

V = π(5)²(10) = 250π cm³, approximately 785.4 cm³.

Front

What is the relationship between the volume of a cone and a cylinder with the same base and height?

Back

The volume of a cone is one-third the volume of a cylinder with the same base and height.

Front

How do you convert the diameter of a cone to radius?

Back

The radius is half of the diameter. If the diameter is d, then r = d/2.

Front

Calculate the volume of a cone with a diameter of 10 m and a height of 4 m.

Back

Radius r = 5 m. V = (1/3)π(5)²(4) = (1/3)π(25)(4) = (100/3)π m³, approximately 104.72 m³.

Front

What is the volume of a sphere with a radius of 7 inches?

Back

V = (4/3)π(7)³ = (4/3)π(343) = 1436.76 in³.

Front

If a cone has a volume of 150.8 in³ and a height of 4 in, what is its radius?

Back

Using V = (1/3)πr²h, we can solve for r: r = sqrt((3V)/(πh)) = sqrt((3*150.8)/(π*4)) ≈ 6 in.