The lateral area of a right cylindrical tank is 288 ft2 and its volume is 1152 ft3. What is the diameter of the cylinder?Group of answer choices12 ft16 ft18 ft8 ft
Question
The lateral area of a right cylindrical tank is 288 ft2 and its volume is 1152 ft3. What is the diameter of the cylinder?Group of answer choices12 ft16 ft18 ft8 ft
Solution
To find the diameter of the cylindrical tank, we can use the formulas for lateral area and volume of a cylinder.
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The formula for the lateral area of a cylinder is given by: Lateral Area = 2πrh, where r is the radius of the cylinder and h is the height.
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The formula for the volume of a cylinder is given by: Volume = πr^2h.
Given that the lateral area is 288 ft^2 and the volume is 1152 ft^3, we can set up the following equations:
Equation 1: 2πrh = 288 Equation 2: πr^2h = 1152
To solve for the diameter, we need to find the value of the radius (r). We can do this by rearranging Equation 1 to solve for h:
h = 288 / (2πr)
Substituting this value of h into Equation 2, we get:
πr^2 * (288 / (2πr)) = 1152
Simplifying the equation, we have:
144r = 1152
Dividing both sides by 144, we find:
r = 8
Therefore, the radius of the cylinder is 8 ft. To find the diameter, we multiply the radius by 2:
Diameter = 2 * 8 = 16 ft.
So, the diameter of the cylindrical tank is 16 ft.
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