Question

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.

Answer 1

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

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

Step 2: write the given sides of the frustum

`B_1=5m*5m=25m^2,B_2=10m*10m=100m^2,\text{altitude}=\text{height=}15m`

Step 3: Calculate the volume of the frustum

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

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