# A baker is serving a new circular brownie pizza dessert (1" thick with a volume of 132.25 cubic inches). What are the dimensions of the open-topped cardboard box needed to serve the brownie pizza (assume the brownie to be inscribed in the box)?

Box measurement is

Given

Since pizza has a circular base, the bottom of the cardboard box will be a square with sides equal to the diameter of the pizza.

Let ‘a’ be the side of the square and ‘h’ the height equal to the thickness of pizza.

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To find the dimensions of the open-topped cardboard box needed to serve the circular brownie pizza, we need to consider the dimensions of the brownie pizza itself.

Given that the brownie pizza has a volume of (132.25 , \text{cubic inches}), and it is (1 , \text{inch}) thick, we can calculate its radius.

The volume ((V)) of a cylinder (which represents the brownie pizza) is given by the formula: [ V = \pi r^2 h ] where (r) is the radius and (h) is the height.

Given that the height ((h)) of the brownie pizza is (1 , \text{inch}), we can rearrange the formula to solve for the radius ((r)): [ r^2 = \frac{V}{\pi h} ] [ r^2 = \frac{132.25}{\pi \times 1} ] [ r^2 = \frac{132.25}{\pi} ] [ r = \sqrt{\frac{132.25}{\pi}} ]

Now that we have the radius of the brownie pizza, we can determine the dimensions of the open-topped cardboard box needed to serve it. Since the brownie pizza is inscribed in the box, the box will have the same diameter as the brownie pizza.

Thus, the dimensions of the open-topped cardboard box needed to serve the circular brownie pizza would be twice the radius of the brownie pizza, giving us: [ \text{Diameter} = 2 \times r ] [ \text{Diameter} = 2 \times \sqrt{\frac{132.25}{\pi}} ]

Therefore, the diameter of the open-topped cardboard box needed to serve the brownie pizza can be calculated using the above expression.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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