find the volume of a frustum of a regular square pyramid the sides of whose bases are 5 meters and 10meters respectively and whose altitude is 15 meters.

Question

29-10-2022
Mathematics

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find the volume of a frustum of a regular square pyramid the sides of whose bases are 5 meters and 10meters respectively and whose altitude is 15 meters.

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MerilynF513198 MerilynF513198 · Answer 1 · 2022-10-29T20:58:23+02:00

SOLUTION

Given the question in the question tab, the following are the soluion steps to get the volume of a frustum of the regular square pyramid

Step 1: Write the formula for the volume of a frustum of the regular square pyramid

[tex]\begin{gathered} V=\frac{h}{3}(B_1+B_2+\sqrt[]{B_1B_2)}_{} \\ \text{where }B_1\text{ and }B_2\text{ are Base areas} \end{gathered}[/tex]

Step 2: write the given sides of the frustum

[tex]B_1=5m\times5m=25m^2,B_2=10m\times10m=100m^2,\text{altitude}=\text{height=}15m[/tex]

Step 3: Calculate the volume of the frustum

[tex]\begin{gathered} V=\frac{h}{3}(B_1+B_2+\sqrt[]{B_1B_2)}_{} \\ \Rightarrow\frac{15}{3}(25+100+\sqrt[]{100(25}) \\ \Rightarrow5(125+\sqrt[]{2500)} \\ \Rightarrow5(125+50) \\ \Rightarrow5(175)=875m^3 \end{gathered}[/tex]

Hence, the volume of the frustum of the regular square pyramid is 875m³