## anonymous 5 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

1. anonymous

2. anonymous

3. anonymous

lol Smiley, what a diagram.

4. anonymous

Smiley, is the base 9 x 9?

5. anonymous

lol i know cant draw as good..

6. anonymous

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. anonymous

8. anonymous

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

9. anonymous

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. anonymous

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. anonymous

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

12. anonymous

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

13. anonymous

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

14. anonymous

So volume is 1134 cubic inches.

15. anonymous

Like I said before, answer c.

16. anonymous

Got it, thanks totally understandable

17. anonymous

Great - become a fan!