Question

pre - algebra ic sem 2 fall 2025
introduction to the volume of a sphere
what can be concluded about the sphere? choose two correct answers.
the radius is half the diameter.
the sphere has a radius of 10 cm.
the formula to apply is $v = \frac{4}{3}bh$.
the diameter measure is substituted into the formula to find the volume.
the volume of the sphere is two - thirds the volume of a cylinder with the same radius and height.

Explanation:

Step1: Analyze the radius - diameter relationship

The basic geometric relationship is \(r=\frac{d}{2}\), where \(r\) is the radius and \(d\) is the diameter. So, the radius is half the diameter.

Step2: Check the radius value

The diameter shown in the image is \(d = 5m\). Using \(r=\frac{d}{2}\), we get \(r=\frac{5}{2}=2.5m
eq10cm\) (since units are inconsistent and value calculation is wrong).

Step3: Analyze the volume formula

The volume formula for a sphere is \(V=\frac{4}{3}\pi r^{3}\), not \(V = \frac{4}{3}Bh\) (where \(V=\frac{4}{3}Bh\) is not a standard sphere - volume formula).

Step4: Analyze the substitution in the formula

We substitute the radius (not the diameter directly) into the volume formula \(V=\frac{4}{3}\pi r^{3}\) (after calculating \(r=\frac{d}{2}\)).

Step5: Analyze the sphere - cylinder volume relationship

The volume of a sphere \(V_s=\frac{4}{3}\pi r^{3}\), and the volume of a cylinder \(V_c=\pi r^{2}h\). If \(h = 2r\) (height of the cylinder equal to the diameter of the sphere), then \(V_s=\frac{2}{3}V_c\) (since \(V_c=\pi r^{2}(2r)=2\pi r^{3}\) and \(\frac{4}{3}\pi r^{3}=\frac{2}{3}(2\pi r^{3})\)).

Answer:

The radius is half the diameter; The volume of the sphere is two - thirds the volume of a cylinder with the same radius and height.