Quadrilateral pyramid

In a regular quadrilateral pyramid, the height is 6.5 cm and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body. Round calculations to 1 decimal place.

Correct result:

S =  273 cm²
V =  225.8 cm³

Solution:

$$\begin{gathered} h=6.5\text{ cm } \\ A=42^{\circ } \\ \tan A=h:(u\mathrm{/}2) \\ u=2\cdot h\mathrm{/}\tan A^{\circ }=2\cdot h\mathrm{/}\tan 42^{\circ }=2\cdot 6.5\mathrm{/}\tan 42^{\circ }=2\cdot 6.5\mathrm{/}0.900404=14.43796\text{ cm } \\ a=u\mathrm{/}\sqrt{2}=14.438\mathrm{/}\sqrt{2}\doteq 10.2092\text{ cm } \\ {S}_1=a^2=10.2092^2\doteq 104.2274{\text{cm}}^2 \\ {h}_2=\sqrt{h^2+(a\mathrm{/}2{)}^2}=\sqrt{6.5^2+(10.2092\mathrm{/}2{)}^2}\doteq 8.2648\text{ cm } \\ {S}_2=a\cdot h_2\mathrm{/}2=10.2092\cdot 8.2648\mathrm{/}2\doteq 42.1884{\text{cm}}^2 \\ S=S_1+4\cdot S_2=104.2274+4\cdot 42.1884=273{\text{cm}}^2 \end{gathered}$$

$V={\displaystyle \frac{1}{3}}\cdot S_1\cdot h={\displaystyle \frac{1}{3}}\cdot 104.2274\cdot 6.5=225.8{\text{cm}}^3$

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Showing 1 comment:

Peachpie1123

Thank u i was trying to find the answer to that in class(my teacher let us look it up and i said it so i got it right.

4 months ago  1 Like Like

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