Question

The figure below shows solid frustum of a pyramid with a square top of side 6cm and a square base of side 10cm. The slant edge of the frustum is 8cm.

1. Calculate the total surface area of the frustum 
2. Calculate the volume of the solid frustum. 
3. Calculate the angle between the planes BCHG and the base EFGH.

Answer 1

1. Calculate the total surface area of the frustum 
   ⁶/₁₀ =^l/_{8 +L}
   12 = L
   Base area = 102 = 100
   Area of 4Δs = 4√25(25-20)(25-20)(25-20)
   = 4√25 x 5 x 5x 15
   = 4√ 9375
   T.S.A of the pyramid = 100 + 387.28
   = 487.28cm²
   Area of the slanting edges of the small pyramid
   = 4√15(3)(3)(9)
   = 139.44
   Surface of the solid frustrum
   = 487 .28 +36-139.44
   383.84
2. Calculate the volume of the solid frustum. (3mks)
   Volume = 1/3 x 100 x 18.71
   = 62.61
   L.S.F = 3/5 ⇒ V.S.F 27/125
   Fraction representing Frustrum
   = 98/125
   ∴Volume of the frustrum = 98/125 x 623.61
   = 488.91
3. Calculate the angle between the planes BCHG and the base EFGH. (3mks)
   tanα=18.71
              5
   α = 75.03º