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A pyramid with triangular base is stack on top of a triangular prism. The pyramid shares a triangular base with the prism. The triangular base has a height of 2 and a base length of 4.4. The height of the prism is 5. The height of the pyramid is 3.9.
Which expression represents the volume of the composite figure?
(2)(4.4)(5) + (2)(4.4)(3.9)
(2)(4.4)(5) – (2)(4.4)(3.9)
One-half(2)(4.4)(5) – One-third (One-half)(2)(4.4)(3.9)
One-half(2)(4.4)(5) + One-third (One-half)(2)(4.4)(3.9)
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Answer: One-half(2)(4.4)(5) + One-third (One-half)(2)(4.4)(3.9)
Reason: Area of the triangular base = (1/2)(2)(4.4). Prism volume = base area × 5 = (1/2)(2)(4.4)(5). Pyramid volume = (1/3)(base area)(3.9) = (1/3)(1/2)(2)(4.4)(3.9). Add them. (If evaluated: base area = 4.4, prism = 22, pyramid = 17.16/3 = 5.72, total = 27.72.)
Reason: Area of the triangular base = (1/2)(2)(4.4). Prism volume = base area × 5 = (1/2)(2)(4.4)(5). Pyramid volume = (1/3)(base area)(3.9) = (1/3)(1/2)(2)(4.4)(3.9). Add them. (If evaluated: base area = 4.4, prism = 22, pyramid = 17.16/3 = 5.72, total = 27.72.)
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