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

How do you find the radius of a sphere if you know the diameter?

Back

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

Front

What is the value of π (Pi) used in volume calculations?

Back

Pi (π) is approximately 3.14, but it can also be represented as 22/7 for calculations.

Front

If a sphere has a radius of 3 cm, what is its volume?

Back

Using the formula V = (4/3)πr³, the volume is V = (4/3)π(3)³ = 36π cm³ or approximately 113.1 cm³.

Front

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

Back

V = (4/3)π(5)³ = (4/3)π(125) = 500/3π in³ or approximately 523.6 in³.

Front

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

Back

The volume increases with the cube of the radius. If the radius doubles, the volume increases by a factor of 8.

Front

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

Back

First, find the radius: r = 10/2 = 5 cm. Then, V = (4/3)π(5)³ = 523.6 cm³.

Front

If the volume of a sphere is 904.32 ft³, what is its radius?

Back

Using the formula V = (4/3)πr³, solve for r: r = ((3V)/(4π))^(1/3). For V = 904.32 ft³, r ≈ 6.2 ft.

Front

What is the relationship between the volume of a sphere and its surface area?

Back

The volume of a sphere is related to its surface area (A = 4πr²). As the radius increases, both volume and surface area increase.

Front

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

Back

To convert cm³ to in³, use the conversion factor: 1 in³ = 16.387 cm³. Divide the volume in cm³ by 16.387.