Answer:
a. S = 6.72 cm
b. A = 1075.70 cm²
c. V = 1,719.1 cm³
Step-by-step explanation:
How to Find
The volume of a frustum of a regular pyramid is equal to one-third of the altitude multiplied by the sum of its bases and the geometric mean between them.
How to Solve
Volume = (1/3)πh (r12 + r22 + (r1 * r2))
Lateral Surface Area
= π(r1 + r2)s = π(r1 + r2)√((r1 - r2)2 + h2)
Top Surface Area = πr12
Base Surface Area = πr22
Total Surface Area
= π(r12 + r22 + (r1 * r2) * s)
= π[ r12 + r22 + (r1 * r2) * √((r1 - r2)2 + h2) ]
To find:
a. the height of the pyramid of which the frustum is a part.
Then, s = 6.7201190465646 cm
In the nearest tenths, the slant height is S = 6.72 cm
b. the surface area of the pyramid.
Then, L = 422.23753255872 cm²
In the nearest tenths, the Surface area of the pyramid is A = 1075.70 cm²
c. the volume of the frustum
Then, V = 1719.0795000443 cm³
Therefore, the volume is 1719.01 cm³ In the nearest tenths
