Janine wants to paint just the sides of a cylindrical pottery vase that has a height of 45 cm and a diameter of16. 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.
Lateral Area: 2π * r * h
2π * 7 * 14 = 196π = 615.75 cm^2
Am I doing it correctly? If so what should be my next step?
Looks good, except the h=45, not 14
2π * 7 * 45 = 630π = 1978.2cm^2 then would that be my final answer?
not bad, except that you did not follow instructions:
To the nearest whole number
Oh, that and the fact that
2π * 7 * 45 = 1979.2
You apparently approximated π by 3.14
Yes, you are on the right track in finding the lateral area. However, there is a small mistake in your calculation. The formula for the lateral area of a cylinder is given by 2πrh, where r is the radius of the base and h is the height of the cylinder.
In this case, the diameter of the vase is given as 14 cm, which means the radius (r) is half of the diameter. So, the radius of the vase is 14/2 = 7 cm. The height (h) of the vase is given as 45 cm.
Now, you can substitute these values into the formula to find the lateral area:
Lateral Area = 2π * r * h
= 2π * 7 * 45
= 630π cm^2
However, the question asks for the answer to be rounded to the nearest whole number. To do this, you need to convert the result to a decimal approximation.
π is approximately equal to 3.14, so you can use this value to get an approximate answer:
Lateral Area ≈ 630 * 3.14
≈ 1972.2 cm^2
To round to the nearest whole number, you can either round up or down depending on the decimal portion:
If the decimal portion is 0.5 or greater, you round up. In this case, it is less than 0.5, so you round down.
Therefore, to the nearest whole number, Janine will need to paint approximately 1972 square centimeters.