A fustrum of a pyramid consists of a square base of length 10cm and a top square base of length 7cm. The height of the fustrum is 6cm. Calculate to the nearest whole number:

Question

I. Surface area
II. Volume

Answer 1

I. Surface Area:
To calculate the surface area of the frustrum, we need to find the area of the two bases and the lateral surface area.

Area of the bottom base = side^2 = 10^2 = 100 cm^2
Area of the top base = side^2 = 7^2 = 49 cm^2

Lateral surface area = 1/2 * (Perimeter of top base + Perimeter of bottom base) * slant height
Lateral surface area = 1/2 * (4 * 7 + 4 * 10) * 6
Lateral surface area = 1/2 * (28 + 40) * 6
Lateral surface area = 1/2 * 68 * 6
Lateral surface area = 204 cm^2

Total Surface Area = Area of bottom base + Area of top base + Lateral surface area
Total Surface Area = 100 + 49 + 204
Total Surface Area = 353 cm^2

II. Volume:
To calculate the volume of the frustrum, we need to find the volume of the frustum which is given by the formula:

Volume = 1/3 * height * (Area of bottom base + Area of top base + sqrt(Area of bottom base * Area of top base))
Volume = 1/3 * 6 * (100 + 49 + sqrt(100 * 49))
Volume = 1/3 * 6 * (100 + 49 + sqrt(4900))
Volume = 1/3 * 6 * (100 + 49 + 70)
Volume = 1/3 * 6 * 219
Volume = 438 cm^3

Therefore, to the nearest whole number:
I. Surface Area = 353 cm^2
II. Volume = 438 cm^3