Question

Asphere has a diameter of 14 units. What is the volume of the sphere in cubic units? If a cylinder has the same radius as the sphere and a height of

14 units, what is the volume of the cylinder? Use 3.14 for
A.
The volume of the sphere is about 1,077.02 cubic units, and the
volume of the cylinder is about 718.01 cubic units
The volume of the sphere is about 1,436 03 cubic units, and the
volume of the cylinder is about 2.154 04 cubic units
C.
The volume of the sphere is about 1,436.03 cubic units, and the
volume of the cylinder is about 957 35 cubic units
D
The volume of the sphere is about 1,077 02 cubic units, and the
volume of the cylinder is about 1,615 53 cubic units

Answer 1

if the diameter is 14, then its radius must be half that, or 7.

`\bf \textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\ \cline{1-1} r=7 \end{cases}\implies V=\cfrac{4\pi (7)^3}{3}\implies \stackrel{\pi =3.14}{V=1436.03} \\\\[-0.35em] ~\dotfill\\\\ \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=7\\ h=14 \end{cases}\implies V=\pi (7)^2(14)\implies \stackrel{\pi =3.14}{V=2154.04}`