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Smiley75
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
lol Smiley, what a diagram.
Smiley, is the base 9 x 9?
lol i know cant draw as good..
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...
I'm thinking it's answer c.
length is 9 and the width is 9 and the height is 12
Volume of the house = (volume of rectangular prism) + (volume of pyramid). Now, for the rectangular prism volume:\[V=(base)(length)(height)=9 \times 9 \times 12=972 inches^3\]
and the volume of the pyramid is given by \[V_{pyramid}=\frac{1}{3}(base_.area)(perpendicular_.height)\]\[=9 \times 9 \times 6 = 486 inches^3\]
The total volume is just the sum of them: 972 in^3 + 486 in^3 = 1458 in^3
wait...I didn't take the third of the base...
\[V_{pyramid}=\frac{1}{3} \times 9 \times 9 \times 6 = 162\]
So volume is 1134 cubic inches.
Like I said before, answer c.
Got it, thanks totally understandable