## 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

1. Smiley75

2. Smiley75

3. lokisan

lol Smiley, what a diagram.

4. lokisan

Smiley, is the base 9 x 9?

5. Smiley75

lol i know cant draw as good..

6. lokisan

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

8. Smiley75

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

9. lokisan

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

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

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

12. lokisan

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

13. lokisan

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

14. lokisan

So volume is 1134 cubic inches.

15. lokisan

Like I said before, answer c.

16. Smiley75

Got it, thanks totally understandable

17. lokisan

Great - become a fan!