Thread: I need help with this Algebraic Models problem

A glass butterfly conservatory is a square-based pyramid. The height of the conservatory is one-half he side of the base. The volume is 900 m^3.

1. Demetra showed how the formula V= 1/6C^3 gives the volume of the conservatory. Explain her thinking include your own diagram.

{V = 1/3 b^2H
=1/3c^2 x 1/2c
=1/3 x 1/2c^2c
=1/6c^3 }

2. a) Describe how to use a formula to determine the height and the side lengths of the base of the butterfly conservatory. Calculate these dimensions to the nearest 10th of a metre.

b) Substitute the dimensions into the formula to check. Are your resuts reasonable? Explain.

3. Describe a different way to determine the side lengths of the base and the height.

4. Suppose the height of the conservatory is doubled, but the base remains the same. Predict what would happen to the volume. Justify your prediction. Check your prediction. Explain how to extend your reasoning to make a generalization about the relationship between the height and the volume of a square-based pyramid.

Thanks in advanced!

Originally Posted by INeedHelpWithMath

A glass butterfly conservatory is a square-based pyramid. The height of the conservatory is one-half he side of the base. The volume is 900 m^3.

1. Demetra showed how the formula V= 1/6C^3 gives the volume of the conservatory. Explain her thinking include your own diagram.

{V = 1/3 b^2H
=1/3c^2 x 1/2c
=1/3 x 1/2c^2c
=1/6c^3 }

I see you did it algebraically, but did you note the geometry of the situation? Given that the height of the pyramid is half the length of one side of the base, can you see how six of these pyramids make a cube whose sides are of length c? This will help with the last question.