Question

MEDAL AND FAN!!!!!!!!!!!
A farmer is building a grain silo for storage. He estimates that will need 256 cubic yards of storage. The grain silo will be shaped as a cube. How long should one side of the grain silo be? (Recall that the volume of a cube is calculated by L^2 , where l is the length of one side).

Answer 1

Remember, volume of a cube is side CUBEd
\[\Large side ^{3}\]
so if \[\Large side ^{3}=256 \rightarrow side=\sqrt[3]{256} \rightarrow side=\sqrt[3]{2^{8}}=\sqrt[3]{2^{6}\times2^{2}}\]
=\[\Large \sqrt[3]{2^{6}\times2^{2}} = \sqrt[3]{2^{6}}\times \sqrt[3]{2^{2}}=2^{2}\times \sqrt[3]{2^{2}}=4\sqrt[3]{4}\]
so the side of the cube with volume 256 is \[\Large 4\sqrt[3]{4}\]

Answer 2

thank you!