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 π (pi) represent in the context of a sphere's volume?

Back

π (pi) is a mathematical constant approximately equal to 3.14, used in calculations involving circles and spheres.

Front

If the radius of a sphere is 5 cm, what is its volume?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3) × 3.14 × (5)³ = 523.3 cm³.

Front

How do you round a number to the nearest tenth?

Back

To round to the nearest tenth, look at the hundredths place. If it's 5 or more, round up; if it's less than 5, round down.

Front

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

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3) × 3.14 × (10)³ = 4186.7 cm³.

Front

What is the volume of a sphere with a radius of 3 inches?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3) × 3.14 × (3)³ = 113.1 in³.

Front

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

Back

The diameter of a sphere is twice the radius. Diameter = 2 × radius.

Front

If a sphere has a volume of 904.3 cm³, what is its radius?

Back

Using the formula V = (4/3)πr³, rearranging gives r = ((3V)/(4π))^(1/3). For V = 904.3 cm³, r ≈ 6.2 cm.

Front

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

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3) × 3.14 × (7)³ = 1436.8 ft³.

Front

How does changing the radius affect the volume of a sphere?

Back

The volume increases with the cube of the radius. Doubling the radius increases the volume by a factor of 8.