Question

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

Modeling
ANSWERED
asked 2021-06-24
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?

Answers (1)

2021-06-25

\(\displaystyle{V}={\left(\frac{{1}}{{3}}\right)}{B}{h}\)
\(\displaystyle{120}={\left(\frac{{1}}{{3}}\right)}{\left({36}\right)}{h}\)
\(120=12h\)
\(10=h\)
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.

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