A right circular cylindrical can is 6 inches high , and the area of its top is 36 square root square inches . What is the minimum number of square inches of construction paper it would take to cover the lateral surface of this can ?
To find the minimum number of square inches of construction paper needed to cover the lateral surface of the can, we need to calculate the lateral surface area of the cylinder.
The lateral surface area of a right circular cylinder can be calculated using the formula:
Lateral Surface Area = 2πrh, where π is the mathematical constant Pi (approximately 3.14159), r is the radius of the cylinder, and h is the height of the cylinder.
In this case, we are given the height of the cylinder, which is 6 inches. We need to find the radius of the cylinder.
To find the radius, we can use the formula for the area of the top of the cylinder:
Area of the Top = πr^2, where r is the radius of the cylinder.
From the given information, the area of the top is 36 square root square inches. Therefore, we can write the equation:
36 square root square inches = πr^2
To solve for r, we divide both sides of the equation by π and then take the square root:
r = √(36 square root square inches / π)
Now that we know the radius, we can substitute the values into the formula for the lateral surface area:
Lateral Surface Area = 2πrh = 2π(√(36 square root square inches / π))(6 inches)
After simplifying the equation, we get:
Lateral Surface Area = 12π√(36 square root square inches / π) square inches
Therefore, the minimum number of square inches of construction paper needed to cover the lateral surface of the can is 12π√(36 square root square inches / π) square inches.