Pyramid cutting calculation

The regular quadrilateral pyramid has a height of 40 cm and a base side of 21 cm. Cut the needle at half the height. How much will both parts have?

Final Answer:

V₁ =  735 cm³
V₂ =  5145 cm³

Step-by-step explanation:

$$\begin{gathered} h=40\text{cm} \\ a=21\text{cm} \\ {S}_1=a^2=21^2=441{\text{cm}}^2 \\ {h}_1=h/2=40/2=20\text{cm} \\ {a}_1=a/2=21/2=\frac{21}{2}=10.5\text{cm} \\ {V}_1=\frac{1}{3}\cdot a_1\cdot a_1\cdot h_1=\frac{1}{3}\cdot 10.5\cdot 10.5\cdot 20=735{\text{cm}}^3 \end{gathered}$$

$$\begin{gathered} V=\frac{1}{3}\cdot a\cdot a\cdot h=\frac{1}{3}\cdot 21\cdot 21\cdot 40=5880{\text{cm}}^3 \\ {V}_2=V-V_1=5880-735=5145{\text{cm}}^3 \end{gathered}$$

Try another example