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Smiley75 Group Title

Kenton stacked a right square pyramid on top of a rectangular prism to create a model house. the dimensions are shown in the diagram. What is the volume of the model house? a. 972 cubic inches b. 1458 cubic inches c. 1134 cubic inches d.648 cubic inches

  • 3 years ago
  • 3 years ago

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  1. Smiley75 Group Title
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    • 3 years ago
  2. Smiley75 Group Title
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    help please

    • 3 years ago
  3. lokisan Group Title
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    lol Smiley, what a diagram.

    • 3 years ago
  4. lokisan Group Title
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    Smiley, is the base 9 x 9?

    • 3 years ago
  5. Smiley75 Group Title
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    lol i know cant draw as good..

    • 3 years ago
  6. lokisan Group Title
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    You need to help me out before I can help. Just write out for me Length = Width = Height = and I'm assuming the perpendicular height for the pyramid is 6 inches...

    • 3 years ago
  7. lokisan Group Title
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    I'm thinking it's answer c.

    • 3 years ago
  8. Smiley75 Group Title
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    length is 9 and the width is 9 and the height is 12

    • 3 years ago
  9. lokisan Group Title
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    Volume of the house = (volume of rectangular prism) + (volume of pyramid). Now, for the rectangular prism volume:\[V=(base)(length)(height)=9 \times 9 \times 12=972 inches^3\]

    • 3 years ago
  10. lokisan Group Title
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    and the volume of the pyramid is given by \[V_{pyramid}=\frac{1}{3}(base_.area)(perpendicular_.height)\]\[=9 \times 9 \times 6 = 486 inches^3\]

    • 3 years ago
  11. lokisan Group Title
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    The total volume is just the sum of them: 972 in^3 + 486 in^3 = 1458 in^3

    • 3 years ago
  12. lokisan Group Title
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    wait...I didn't take the third of the base...

    • 3 years ago
  13. lokisan Group Title
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    \[V_{pyramid}=\frac{1}{3} \times 9 \times 9 \times 6 = 162\]

    • 3 years ago
  14. lokisan Group Title
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    So volume is 1134 cubic inches.

    • 3 years ago
  15. lokisan Group Title
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    Like I said before, answer c.

    • 3 years ago
  16. Smiley75 Group Title
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    Got it, thanks totally understandable

    • 3 years ago
  17. lokisan Group Title
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    Great - become a fan!

    • 3 years ago
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