Question

which object is best modeled by a sphere when determining volume?
a. cone
b. water bottle
c. marble
d. gift box
which has a larger volume: a cylinder with a radius of 5 cm and a height of 12 cm, or a sphere with a radius of 5 cm?
a. sphere by 62.8 cm
b. cylinder by 188.4 cm
c. both have the same volume
d. cylinder by 418.9 cm

Explanation:

Step1: Volume formula of cylinder

The volume formula of a cylinder is \(V_{cylinder}=\pi r^{2}h\). Given \(r = 5\space cm\) and \(h=12\space cm\), then \(V_{cylinder}=\pi\times5^{2}\times12=\pi\times25\times12 = 300\pi\space cm^{3}\approx300\times3.14=942\space cm^{3}\)

Step2: Volume formula of sphere

The volume formula of a sphere is \(V_{sphere}=\frac{4}{3}\pi r^{3}\). Given \(r = 5\space cm\), then \(V_{sphere}=\frac{4}{3}\pi\times5^{3}=\frac{4}{3}\pi\times125=\frac{500}{3}\pi\space cm^{3}\approx\frac{500}{3}\times3.14\approx523.3\space cm^{3}\)

Step3: Calculate the difference

\(V_{cylinder}-V_{sphere}=942 - 523.3=418.7\approx418.9\space cm^{3}\)

Answer:

d. Cylinder by \(418.9\space cm^{3}\)