Question

in his science class, pato is using clay to make scale spherical models of several planets in the solar system. the table below shows the dimensions for each model planet he will make.

what percent of the total volume of clay that he uses will be for the model of mars?

round your answer to the nearest percent.

Explanation:

Step1: Calculate the volume of each planet model

The volume formula for a sphere is \(V = \frac{4}{3}\pi r^{3}\).
For Mercury (\(r = 7.4\)): \(V_{Mercury}=\frac{4}{3}\pi(7.4)^{3}=\frac{4}{3}\pi\times405.224\)
For Venus (\(r = 6\)): \(V_{Venus}=\frac{4}{3}\pi(6)^{3}=\frac{4}{3}\pi\times216\)
For Earth (\(r = 6.3\)): \(V_{Earth}=\frac{4}{3}\pi(6.3)^{3}=\frac{4}{3}\pi\times250.047\)
For Mars (\(r = 3.3\)): \(V_{Mars}=\frac{4}{3}\pi(3.3)^{3}=\frac{4}{3}\pi\times35.937\)

Step2: Calculate the total volume

\(V_{total}=V_{Mercury}+V_{Venus}+V_{Earth}+V_{Mars}\)
\(V_{total}=\frac{4}{3}\pi(405.224 + 216+250.047 + 35.937)=\frac{4}{3}\pi\times907.208\)

Step3: Calculate the percentage for Mars

The percentage \(P=\frac{V_{Mars}}{V_{total}}\times100\)
Since \(\frac{V_{Mars}}{V_{total}}=\frac{\frac{4}{3}\pi\times35.937}{\frac{4}{3}\pi\times907.208}=\frac{35.937}{907.208}\)
\(P=\frac{35.937}{907.208}\times100\approx 4\)

Answer:

\(4\)