Question

select the correct answer. a sphere 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 π. a. the volume of the sphere is about 1077.02 cubic units, and the volume of the cylinder is about 718.01 cubic units. b. the volume of the sphere is about 1436.03 cubic units, and the volume of the cylinder is about 2154.04 cubic units. c. the volume of the sphere is about 1436.03 cubic units, and the volume of the cylinder is about 957.35 cubic units. d. the volume of the sphere is about 1077.02 cubic units, and the volume of the cylinder is about 1615.53 cubic units.

Explanation:

Step1: Find the radius of the sphere and cylinder

The diameter of the sphere (and cylinder) is 14 units, so the radius $r=\frac{14}{2}=7$ units. The height of the cylinder $h = 14$ units.

Step2: Calculate the volume of the cylinder

The volume formula for a cylinder is $V_{cylinder}=\pi r^{2}h$. Substitute $r = 7$ and $h=14$ into the formula: $V_{cylinder}=3.14\times7^{2}\times14=3.14\times49\times14 = 3.14\times686=2154.04$ cubic units.

Step3: Calculate the volume of the sphere

The volume formula for a sphere is $V_{sphere}=\frac{4}{3}\pi r^{3}$. Substitute $r = 7$ into the formula: $V_{sphere}=\frac{4}{3}\times3.14\times7^{3}=\frac{4}{3}\times3.14\times343=\frac{4\times3.14\times343}{3}=\frac{4308.08}{3}\approx1436.03$ cubic units.

Answer:

The volume of the sphere is about 1436.03 cubic units, and the volume of the cylinder is about 2154.04 cubic units. So the correct answer is B.