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!