Question

a sphere has a diameter of 8 cm. which statements about the sphere are true? choose three correct answers.
the radiuss length is twice the length of the diameter.
the volume of the sphere is \frac{2048}{3}\pi cm^{3}.
the volume of the sphere is \frac{256}{3}\pi cm^{3}.
the sphere has a radius of 16 cm.
the sphere has a radius of 4 cm.
the diameters length is twice the length of the radius.

Explanation:

Step1: Calculate the radius

Given diameter \(d = 8\) cm. Since \(r=\frac{d}{2}\), then \(r=\frac{8}{2}=4\) cm.

Step2: Calculate the volume of the sphere

The formula for the volume of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 4\) into the formula:

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Also, by the definition of diameter and radius (\(d = 2r\)), the diameter's length is twice the length of the radius.

Answer:

• The volume of the sphere is \(\frac{256}{3}\pi\space\text{cm}^{3}\).
• The sphere has a radius of \(4\) cm.
• The diameter's length is twice the length of the radius.