How to find the surface area of a cylinder with a diameter of 6ft and a height of 20cm using 3.14 rounded to the nearest whole number. (I cant figure it out my book doesn't give an example of it just a radius formula and ive tried searching the formula but i cant find any websites that show me how to do it or whats the formula) please help.
omg just give the answer u retuards
Area of a circle = d ^ 2 * pi / 4
Circumference of a circle = d * pi
Area of a rectangle = Circumference * height = d * pi * h
Area of a cylinder = 2 * Area of a circle + Area of a rectangle
A = 2 * d ^ 2 * pi / 4 + d * pi * h
So :
A = 2 * d ^ 2 * pi / 4 + d * pi * h =
d ^ 2 * pi / 2 + d * pi * h =
d * pi * ( d / 2 + h )
A = d * pi * ( d / 2 + h )
______________________________
Remark:
r = d / 2
A = d * pi * ( d / 2 + h ) is equivalent of:
A = 2 * r * pi * ( r + h )
____________________________
pi rounded to the nearest whole number = 3
1 in = 2.54 cm
1 ft = 12 in = 12 * 3.54 = 30.48 cm
6 ft = 6 * 30.48 = 182.88 cm
Now you can calculate the surface area of a cylinder
Surface Area
A = 2•pi•r^2 + 2•pi•r•h
The radius is half the diameter
2(3.14)3^2 + 2(3.14)3•20
56.52 + 376.8 = 433.32
A = 433cm
Explanation
r = d / 2
d = 2 r
For that reason
A = d * pi * ( d / 2 + h ) =
2 * r * pi * ( r + h )
thank you guys I figured it out! and especially to Chelle (:.
To find the surface area of a cylinder, you need to know its height and diameter (or radius). Let's break down the steps to calculate it using the given values:
Step 1: Find the radius of the cylinder.
The diameter is given as 6 feet, but we need the radius. The radius is half the diameter of the cylinder. So, divide the diameter by 2:
Radius = Diameter/2 = 6ft/2 = 3ft.
Step 2: Calculate the lateral surface area.
The lateral surface area of a cylinder can be found by multiplying the circumference of the base by the height. The circumference can be calculated using the formula C=2πr, where C is the circumference and r is the radius. The given value of π is 3.14, rounded to the nearest whole number, which is 3. So, the formula becomes C=2(3)(3ft) = 18ft.
Now, multiply the calculated circumference by the height: Lateral Surface Area = C × h = 18ft × 20cm.
Step 3: Calculate the top and bottom surface areas.
To find the top and bottom surface areas (also called the base areas), use the formula A = πr^2, where A is the area and r is the radius. Square the radius by multiplying it by itself: r^2 = (3ft)^2 = 9ft^2.
Now, multiply the squared radius by π: Base Area = A = π × r^2 = 3 × 9ft^2.
Step 4: Calculate the total surface area.
Finally, add the lateral surface area and the sum of the top and bottom surface areas to find the total surface area of the cylinder.
Total Surface Area = Lateral Surface Area + 2 × Base Area.
Now, substituting the values into the formula, we have:
Total Surface Area = 18ft × 20cm + 2 × 3 × 9ft^2.
Please note that you need to convert the height from centimeters to feet to ensure consistent units in the calculation.
Simplify and calculate the final result to find the total surface area of the cylinder.