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Smiley75

  • 3 years ago

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

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

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

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

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

  6. lokisan
    • 3 years ago
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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...

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

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

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

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

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

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

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

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

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

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

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

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