Pressing a circular cookie cutter over a tray of 1 inch x 1 inch x 1 inch fudge cubes creates a cylinder. If the cylinder consists of approximately 12.6 fudge cubes, what is the approximate area of the cylinder's base?
PLEASE HELP!!
v = Bh
so,
12.6 = B*1
Thank you so so much!!!
To find the approximate area of the cylinder's base, we need to determine the number of fudge cubes that make up the base.
Given that the height of each cube is 1 inch, the cylinder's base corresponds to the width and length of the fudge cubes.
Since the circular cookie cutter is pressed over the tray and each cube has dimensions of 1 inch x 1 inch, the area of the base would be the same as that of a circle with a diameter of 1 inch.
The formula for calculating the area of a circle is A = πr^2, where A is the area and r is the radius.
In this case, the diameter is 1 inch, so the radius would be 1/2 inch.
Plugging in the values, we have:
A = π(1/2)^2
A = π(1/4)
A ≈ 0.785 square inches
Therefore, the approximate area of the cylinder's base is approximately 0.785 square inches.
To calculate the approximate area of the cylinder's base, we need to first find the radius of the circular cookie cutter and then use that to calculate the area of the base.
1. Find the volume of one fudge cube:
Since each fudge cube's dimensions are 1 inch x 1 inch x 1 inch, the volume of one fudge cube is 1 cubic inch (1 in^3).
2. Determine the volume of the cylinder:
The given information states that the cylinder consists of approximately 12.6 fudge cubes. Since each cube has a volume of 1 cubic inch, the volume of the cylinder is approximately 12.6 cubic inches.
3. Calculate the radius of the circular cookie cutter:
The formula for the volume of a cylinder is V = πr^2h, where V is the volume, r is the radius, and h is the height.
Since we know the number of fudge cubes in the cylinder (12.6) and the volume of one fudge cube (1 cubic inch), we can rearrange the formula to solve for the radius as follows:
12.6 = πr^2 x 1
12.6 = πr^2
r^2 = 12.6 / π
r ≈ sqrt(4.01) ≈ 2.003
4. Calculate the area of the cylinder's base:
The area of the base of a cylinder is given by the formula A = πr^2, where A is the area and r is the radius.
Substituting the calculated radius into the formula, we can find the approximate area of the cylinder's base:
A ≈ π x (2.003)^2
A ≈ π x 4.012 ≈ 12.6 square inches (approximately)
Therefore, the approximate area of the cylinder's base is 12.6 square inches.