Which has more volume: a 10-inch-tall can with a diameter of 10 inches or a 7×10×10 inch box?


The comparison is made between 2 solids, one cylindrical and the other a rectangular box.
Volume of the can \(=\pi / 4 \times D^{2} \times H\), where H is the height of the can
\(V=\pi/ 4 \times D^{2} \times 10=10 \pi / 4 \times 100=2.5 \pi \times 100\)
Volume of the box = LWH
\(V=10 \times 10 \times 7=7 \times 100\)
Comparing the two volumes:
Volume of the can ? Volume of the box

\(2.5 \pi \times 100 ? 7 \times 100\)
7.5 is bigger than 7 Using: \(\pi=3\)
Therefore, the can has a bigger volume than the box.

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