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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
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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lokisanBest ResponseYou've already chosen the best response.0
lol Smiley, what a diagram.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Smiley, is the base 9 x 9?
 3 years ago

Smiley75Best ResponseYou've already chosen the best response.0
lol i know cant draw as good..
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
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...
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
I'm thinking it's answer c.
 3 years ago

Smiley75Best ResponseYou've already chosen the best response.0
length is 9 and the width is 9 and the height is 12
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Volume of the house = (volume of rectangular prism) + (volume of pyramid). Now, for the rectangular prism volume:\[V=(base)(length)(height)=9 \times 9 \times 12=972 inches^3\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
and the volume of the pyramid is given by \[V_{pyramid}=\frac{1}{3}(base_.area)(perpendicular_.height)\]\[=9 \times 9 \times 6 = 486 inches^3\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
The total volume is just the sum of them: 972 in^3 + 486 in^3 = 1458 in^3
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
wait...I didn't take the third of the base...
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
\[V_{pyramid}=\frac{1}{3} \times 9 \times 9 \times 6 = 162\]
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
So volume is 1134 cubic inches.
 3 years ago

lokisanBest ResponseYou've already chosen the best response.0
Like I said before, answer c.
 3 years ago

Smiley75Best ResponseYou've already chosen the best response.0
Got it, thanks totally understandable
 3 years ago
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