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

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

2.

a. a = 12 cm

b. V = 384 cm^3

Explanation:

1. The volume of rectangular pyramid is given by:

`V=(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-((a)/(2))^2}=\sqrt{4a^2-(a^2)/(4)}\\\\h=√(15)(a)/(2)`

The, the volume is:

`V=(1)/(3)(a^2)(√(15)(a)/(2))=(a^3)/(6)√(15)`

2.

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

`(a)/(2)=√((10cm)^2-(8cm)^2)=6cm\\\\a=12cm`

b. The volume is given by:

`V=(1)/(3)(12cm)^2(8cm)=384\ cm^3`