# Marilda has a block of modeling clay that is 8 inches by 5 inches by 3 inches. She is experimenting with different shapes that can be made from the cl

Marilda has a block of modeling clay that is 8 inches by 5 inches by 3 inches. She is experimenting with different shapes that can be made from the clay. Give your answers to the nearest tenth. Suppose Marilda wants to make a square pyramid with a 6 by 6 in. base. How tall would it be?

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delilnaT

$$\displaystyle{V}={\left(\frac{{1}}{{3}}\right)}{B}{h}$$
$$\displaystyle{120}={\left(\frac{{1}}{{3}}\right)}{\left({36}\right)}{h}$$
$$120=12h$$
$$10=h$$
From part (a), the volume of the clay is $$120 \ln^3$$. Let the volume of the pyramid be $$V=120 \ln^3$$. If the square base has dimensiont of 6 in, by 6 in, then it has an area of $$B=6^2=36 \ln^2$$. Substitute in the volume and area of the base into the formula for the volume of a pyramid. Then solve for h.