Janine wants to paint just the sides of a cylindrical pottery vase that has a height of 45 cm and a diameter of 14 cm. To the nearest whole number, find the number of square centimeters she will need to paint. Explain the method you would use to find the lateral area.
Thank you Reiny!
The surface area of the side of a cylinder is
2πrh, in effect, the circumference of the circle times the height.
(Visualize taking a piece of paper and forming it into a cylinder.)
So for yours, the radius is 7 cm
surface area = 2π(7)(45) = appr 1979 cm^2
To find the lateral area of the cylindrical pottery vase, we need to calculate the surface area of the curved part of the vase, excluding the top and bottom.
The formula for the lateral area of a cylinder is given by:
Lateral Area = 2πrh
where π is a mathematical constant approximately equal to 3.14159, r is the radius of the cylinder (half the diameter), and h is the height of the cylinder.
First, let's find the radius of the vase using the given diameter, which is 14 cm. The radius is half of the diameter, so we divide it by 2:
Radius (r) = 14 cm / 2 = 7 cm
Next, we substitute the values of the radius (r) and height (h) into the formula to calculate the lateral area:
Lateral Area = 2π * 7 cm * 45 cm
Now, we calculate the value of 2π * 7 cm * 45 cm using a calculator or by multiplying:
Lateral Area ≈ 2 * 3.14159 * 7 cm * 45 cm
Lateral Area ≈ 6.28318 * 7 cm * 45 cm
Lateral Area ≈ 19.63485 * 7 cm * 45 cm
Lateral Area ≈ 28.29818 * 45 cm
Lateral Area ≈ 1273.417 cm²
Therefore, the number of square centimeters Janine will need to paint is approximately 1273 cm². Rounding to the nearest whole number, the answer is 1273 cm².