Question

The edges of the bases of the frustum of a regular square pyramid have length 5 and 9, and the slant height of the frustum is 6. What is the:
VOLUME OF THE FRUSTUM

SURFACE AREA OF THE FRUSTUM


I NEED HELP PLEASE PLEASE PLEASE

Answer 1

Answer:

Volume of the frustum = 225.0952

Surface area = 274

Step-by-step explanation:

The volume can be calculated as the difference of the complete pyramid and the tip of the pyramid.

To find the height of the frustum, we can use pythagoras theorem in the following triangle:

first side: 9 - 5 = 4

second side h (height)

hypotenusa: slang = 6

6^2 = h^2 + 4^2

h^2 = 36 - 16 = 20

h = 4.4721

To find the height of the complete pyramid (H), we can use the following rule of three:

H / 9 = (H - 4.4721) / 5

5H = 9H - 40.2489

4H = 40.2489

H = 10.0622

Volume of complete pyramid:

V_complete = (1/3)*9^2*10.0622 = 271.6794

Volume of the tip:

V_tip = (1/3)*5^2*(10.0622 - 4.4721) = 46.5842

Volume of the frustum:

V_frustum = V_complete - V_tip = 225.0952

The surface area is the bigger base area + smaller base area + four side areas.

Bigger base area = 9^2 = 81

Smaller base area = 5^2 = 25

Side area = (9+5)*6/2 = 42

Total surface area: 81 + 25 + 4*42 = 274