Volume of Spheres

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 of the sphere.

Front

What does the symbol π (Pi) represent in mathematics?

Back

π (Pi) is a mathematical constant approximately equal to 3.14, representing the ratio of the circumference of a circle to its diameter.

Front

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

Back

If the radius is doubled, the volume increases by a factor of 8, since volume is proportional to the cube of the radius.

Front

Calculate the volume of a sphere with a radius of 3 cm using π = 3.14.

Back

The volume is V = (4/3) * 3.14 * (3)³ = 113.04 cm³.

Front

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

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3) * 3.14 * (7)³ = 1436.76 m³.

Front

How do you convert the volume of a sphere from cubic inches to cubic centimeters?

Back

To convert cubic inches to cubic centimeters, multiply by 16.387 (1 in³ = 16.387 cm³).

Front

What is the volume of a sphere with a radius of 10 inches?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3) * 3.14 * (10)³ = 4186.67 in³.

Front

If a sphere has a volume of 904.8 cubic yards, what is its radius?

Back

Using the formula V = (4/3)πr³, the radius can be found by rearranging the formula: r = ((3V)/(4π))^(1/3). For V = 904.8, r ≈ 6.24 yards.

Front

What is the relationship between the diameter and radius of a sphere?

Back

The diameter of a sphere is twice the radius. d = 2r.

Front

What is the volume of a sphere with a radius of 5 meters?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3) * 3.14 * (5)³ = 523.33 m³.