IDNStudy.com, ang iyong gabay para sa maaasahan at mabilis na mga sagot. Makakuha ng mga sagot sa iyong mga tanong mula sa aming mga eksperto, handang magbigay ng mabilis at tiyak na solusyon.

A regular square pyramid has a base whose area is 25 sq. In. A section parallel to the base and 3.18 in above it has an area of 4 sq. In. Find the ratio of the volume tp the frustum tp the volume of the pyramid

Sagot :

Given:
H = 3.18 in
B = 25 in^2
b = 4 in^2

Req'd: Vfrustum/Vpyramid

Using ratio & proportion..
HP = 3.18 + hp

HP/hp = 5/2
3.18 + hp / hp = 5/2
(3.18 + hp) 2 = 5hp
6.36 + 2hp = 5hp
6.36 = 3hp
2.12 = hp

So, HP = 3.18 + 2.12
HP = 5.3

Vpyramid = BH/3
BH/3 = (25*5.3) / 3
Vpyramid = 44.1667 in^3

Vfrustum = H/3 [B + b + sqrt of Bb]
= 3.18in/3 [25in^2 + 4in^2 + sqrt of 100in^4]
= 3.18in/3 [ 29in^2 + 10in^2]
= 3.18in/3 (39in^2)
Vfrustum = 41.34 in^3

Req'd: Vfrustum / Vpyramid
41.34 in^3 / 44.1667 in^3