Question

1.....O piramida triunghiulara regulata are latura bazei a si muchia laterala 2a. Sa se afle volumul si aria laterala a piramidei.




2...O piramida patrulatera regulata are muchia laterala de 10cm si inaltimea de 8.se cer:



a)Latura bazei



b)Volumul piramidei



Repede dau funda :)

Answer 1

Answer:

1. a^3/6 (15)^{1/2}

2.

a. a = 12 cm

b. V = 384 cm^3

Step-by-step explanation:

1. The volume of rectangular pyramid is given by:

$V=\frac{1}{3}bh$

b: base area = a^2

h: height

c: side edge = 2a

"h" can be calculated by using the Pitagora's theorem:

$h=\sqrt{(2a)^2-(\frac{a}{2})^2}=\sqrt{4a^2-\frac{a^2}{4}}\\\\h=\sqrt{15}\frac{a}{2}$

The, the volume is:

$V=\frac{1}{3}(a^2)(\sqrt{15}\frac{a}{2})=\frac{a^3}{6}\sqrt{15}$

2.

a. The side base is calculated by using the Pitagora's theorem again:

$\frac{a}{2}=\sqrt{(10cm)^2-(8cm)^2}=6cm\\\\a=12cm$

b. The volume is given by:

$V=\frac{1}{3}(12cm)^2(8cm)=384\ cm^3$