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
