Quadrilateral 30401

Calculate the volume of a regular quadrilateral pyramid, given:
1) a = 3.5 m; vt = 24 dm
Express the volume in m³ and round to 1 decimal place
2) a = 1.6 dm; vt = 295 mm
Calculate the volume in cm³ and round to 1 decimal place

Solution entry:
1) entry
2) sample
3) substitution
4) calculation

Correct answer:

V₁ =  9.8 m³
V₂ =  2517.3 cm³

Step-by-step explanation:

$$\begin{gathered} a_1=3.5\text{m} \\ {v}_1=24\text{dm}\to \text{m}=24:10\text{m}=2.4\text{m} \\ {S}_1=a_1^2=3.5^2=\frac{49}{4}=12.25{\text{m}}^2 \\ {V}_1=\frac{1}{3}\cdot S_1\cdot v_1=\frac{1}{3}\cdot \frac{49}{4}\cdot \frac{12}{5}=\frac{49}{5}{\text{m}}^3=9.8{\text{m}}^3 \end{gathered}$$

$$\begin{gathered} a_2=1.6\text{dm}\to \text{cm}=1.6\cdot 10\text{cm}=16\text{cm} \\ {v}_2=295\text{mm}\to \text{cm}=295:10\text{cm}=29.5\text{cm} \\ {S}_2=a_2^2=16^2=256{\text{cm}}^2 \\ {V}_2=\frac{1}{3}\cdot S_2\cdot v_2=\frac{1}{3}\cdot 256\cdot \frac{59}{2}=\frac{7552}{3}{\text{cm}}^3=2517.3{\text{cm}}^3 \end{gathered}$$

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