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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

2. Smiley75 Group Title

help please

3. lokisan Group Title

lol Smiley, what a diagram.

4. lokisan Group Title

Smiley, is the base 9 x 9?

5. Smiley75 Group Title

lol i know cant draw as good..

6. lokisan Group Title

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 Group Title

I'm thinking it's answer c.

8. Smiley75 Group Title

length is 9 and the width is 9 and the height is 12

9. lokisan Group Title

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 Group Title

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 Group Title

The total volume is just the sum of them: 972 in^3 + 486 in^3 = 1458 in^3

12. lokisan Group Title

wait...I didn't take the third of the base...

13. lokisan Group Title

$V_{pyramid}=\frac{1}{3} \times 9 \times 9 \times 6 = 162$

14. lokisan Group Title

So volume is 1134 cubic inches.

15. lokisan Group Title

Like I said before, answer c.

16. Smiley75 Group Title

Got it, thanks totally understandable

17. lokisan Group Title

Great - become a fan!