large pizza at Tony's pizza is a circle with a 14 inch diameter it's box is a rectangular prism that is 14 1/8 inches long 14 1/8 inches wide and 1 3/4 inches tall you have to create a new shape for the pizza but it has to have at least 5 sides and be cut into equal slices. Please show all of your work
All I need is to prove that the box is about the same surface area as Tony's large pizza. And that the pizza will fit in the box
Surface area of the pizza = πr2
= 3.14 x (7 inches)2
= 3.14 x 49
= 153.86 in2
Surface area of the box = 2(14 1/8 x 14 1/8) + 2(14 1/8 x 1 3/4) + 2(1 3/4 x 14 1/8)
= 2(198.06) + 2(25.06) + 2(24.75)
= 396.12 + 50.12 + 49.50
= 495.74 in2
The surface area of the box is slightly larger than the surface area of the pizza, so the pizza will fit in the box.
Weird!!!
since the box is 14 1/2 by 14 1/2, and the diameter of the pizza
is 14, it will fit.
To determine if the box is about the same surface area as the large pizza, we can first calculate the surface area of the pizza and then compare it to the surface area of the box.
1. Surface Area of the Pizza:
The pizza is in the shape of a circle, so we can calculate its surface area using the formula for the area of a circle, which is A = πr², where r is the radius.
Given that the pizza has a diameter of 14 inches, the radius (r) is half the diameter, so r = 14 / 2 = 7 inches.
Substituting the value of the radius into the formula, we get:
A = π * (7 inches)²
A = 49π square inches (approximately 153.94 square inches)
2. Surface Area of the Box:
The box is in the shape of a rectangular prism, so we can calculate its surface area using the formula for the surface area of a rectangular prism, which is A = 2lw + 2lh + 2wh, where l is the length, w is the width, and h is the height.
Given that the length (l) and width (w) of the box are 14 1/8 inches, and the height (h) is 1 3/4 inches, we can substitute these values into the formula to calculate the surface area:
A = 2 * (14 1/8 inches * 14 1/8 inches) + 2 * (14 1/8 inches * 1 3/4 inches) + 2 * (14 1/8 inches * 1 3/4 inches)
A = 2 * (200 1/64 square inches) + 2 * (24 43/64 square inches) + 2 * (24 43/64 square inches)
A = 400 2/64 square inches + 49 86/64 square inches + 49 86/64 square inches
A = 499 2/64 square inches + 99 172/64 square inches
A = 598 174/64 square inches (approximately 613.78 square inches)
Comparing the surface area of the pizza (approximately 153.94 square inches) with the surface area of the box (approximately 613.78 square inches), we can conclude that the box is much larger than the pizza, and therefore the pizza will fit comfortably inside the box.
To prove that the box is about the same surface area as Tony's large pizza, we need to calculate the surface area of both shapes and compare them.
First, let's calculate the surface area of the pizza. Given the diameter of the pizza is 14 inches, the radius (r) can be calculated by dividing the diameter by 2:
r = 14 inches / 2 = 7 inches
The formula to calculate the surface area (A) of a circle is:
A = πr^2
where π is a mathematical constant approximately equal to 3.14159.
Now let's plug in the values:
A = 3.14159 * (7 inches)^2
≈ 3.14159 * 49 square inches
≈ 153.938 square inches (rounded to three decimal places)
So, the surface area of the pizza is approximately 153.938 square inches.
Now let's calculate the surface area of the box. The formula for the surface area (A) of a rectangular prism is:
A = 2lw + 2lh + 2wh
where l, w, and h represent the length, width, and height, respectively.
Plugging in the given values:
A = 2 * (14 1/8 inches * 14 1/8 inches) + 2 * (14 1/8 inches * 1 3/4 inches) + 2 * (14 1/8 inches * 1 3/4 inches)
= 2 * (199.750625 square inches) + 2 * (24.78125 square inches) + 2 * (24.78125 square inches)
= 399.50125 square inches + 49.5625 square inches + 49.5625 square inches
= 498.62625 square inches (rounded to five decimal places)
So, the surface area of the box is approximately 498.62625 square inches.
Comparing the surface areas, we can see that the box has a larger surface area than the pizza, which indicates that the pizza will indeed fit inside the box.
Please note that the calculations are approximations due to the rounding of decimal places for simplicity purposes.