Volume of Spheres + Composite Figures Practice

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 volume of a sphere with a radius of 3 cm?

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 a composite figure?

Back

A composite figure is a shape that is made up of two or more simple shapes, such as rectangles, triangles, and circles.

Front

How do you calculate the volume of a composite figure that includes a sphere and a cylinder?

Back

Calculate the volume of each shape separately and then add them together. For example, V_total = V_sphere + V_cylinder.

Front

What is the volume of a cylinder with a radius of 5 cm and a height of 10 cm?

Back

The volume V of a cylinder is given by V = πr²h. So, V = π(5)²(10) = 250π cm³ or approximately 785.4 cm³.

Front

If a sphere has a volume of 500 cm³, how do you find its radius?

Back

Rearranging the volume formula V = (4/3)πr³ gives r = ((3V)/(4π))^(1/3). For V = 500 cm³, r ≈ 5.42 cm.

Front

What is the volume of a half sphere with a radius of 4 cm?

Back

The volume of a half sphere is half of the full sphere's volume. V_half = (1/2)(4/3)πr³ = (2/3)π(4)³ = (128/3)π cm³ or approximately 134.04 cm³.

Front

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

Back

To convert diameter to radius, divide the diameter by 2.

Front

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

Back

First, find the radius: r = 10/2 = 5 inches. Then, V = (4/3)π(5)³ = (500/3)π in³ or approximately 523.6 in³.