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Vedmedyk [2.9K]
3 years ago
10

Sara has a stack of 8 plates, each plate is 0.5 inches tall and she is trying to wrap them as a gift.

Mathematics
1 answer:
AlekseyPX3 years ago
5 0

Answer:

The plates will not fit into the box.

Step-by-step explanation:

Each plate is 0.5 inches tall; therefore, the stack of 8 plates will have a height of 0.5in*8 = 4inches.

Also, the diameter of the largest plate is 10 inches or has a radius of 5 inches, which matches the radius of the cylindrical box; therefore, we know that the stack of plates can fit into the base area of the cylindrical box.

What we want to figure out now is the height of the cylindrical box <em>to see if it is greater than or equal to 4 inches</em>—<em>the height of the stack of plates. </em>

The volume of a cylinder is \pi R^2h, and since for our cylindrical box the volume is 150 cubic inches; therefore,

\pi R^2h = 150in^3

putting in R = 5in and solving for height h we get

h = \dfrac{150in^3}{\pi (5)^2}

h = 1.91\: inches,

which is not greater than 4 inches, which means the plates will not fit into the box since the height of the stack is greater than the height of the box.

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