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Question:
1212The comparison is made between two solids, one a cylinder (the can) and the other a rectangular box. To help us visualize the comparison, let's use these sketches:
The formula for the volume of a cylinder is:
Volume = \uD835\uDF0B \u00D7
\u00D7 H, where H is the height of the cylinder
The problem does not provide the radius. Instead, it gives the diameter as 10. We know that the radius of a circle is 1/2 of its diameter, or:
r =
inches
We go back to the formula for volume and plug in the values r = 5 and \uD835\uDF0B = 3.14:
Volume = 3.14 \u00D7
\u00D7 10 = 785 cubic inches
Notes: We may actually directly solve for the volume using the formula V =
\u00D7
\u00D7 H and get the same answer.
Now, we're ready to solve for the volume of the box:
Volume = length \u00D7 width \u00D7 height = 10 \u00D7 10 \u00D7 7 = 700 cubic inches
Now, we see that the volume of the can is greater than that of the box.
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