A pizza shop is considering increasing the diameter of its family pizza tray from 32 cm to 34 cm. Find the percentage increase in area, correct to two decimal places, from the 32 cm tray to the 34 cm tray.
How did you get this working out? would you mind showing this step by step? :)
Reply to @Hope,
I know this is 1 year later, but if you're still stuck he put this equation into a calculator then pressed the S to D button to transform it from a fraction to a decimal hope this helps.
Well, let me put on my clown shoes and calculate that for you! The formula to calculate the area of a circle is A = π * r^2. By using this formula, we can find the area of the 32 cm tray as A1 = π * (16^2) and the area of the 34 cm tray as A2 = π * (17^2). Now let's do some math and find the percentage increase in area:
Percentage Increase = ((A2 - A1) / A1) * 100
= ((π * (17^2) - π * (16^2)) / (π * (16^2))) * 100
= ((289 - 256) / 256) * 100
= (33 / 256) * 100
≈ 12.89%
So, the percentage increase in area, from the 32 cm tray to the 34 cm tray, is approximately 12.89%. Now that's one big pie!
@hope thanks
To find the percentage increase in area, we need to calculate the area of the 32 cm tray and the area of the 34 cm tray, and then find the percentage increase.
The formula for the area of a circle is A = πr^2, where A is the area and r is the radius.
First, let's find the area of the 32 cm tray:
- The radius would be half the diameter, so the radius of the 32 cm tray is 32 cm / 2 = 16 cm.
- Now we can calculate the area using the formula: A = π(16 cm)^2.
Next, let's find the area of the 34 cm tray:
- The radius of the 34 cm tray would be 34 cm / 2 = 17 cm.
- We can calculate the area using the formula: A = π(17 cm)^2.
Now, let's calculate the percentage increase in area:
- First, find the difference in area by subtracting the area of the 32 cm tray from the area of the 34 cm tray.
- Then divide the difference by the area of the 32 cm tray.
- Multiply the result by 100 to convert it to a percentage.
Let's calculate everything step by step:
1. Area of the 32 cm tray: A1 = π(16 cm)^2.
2. Area of the 34 cm tray: A2 = π(17 cm)^2.
3. Difference in area: ΔA = A2 - A1.
4. Percentage increase in area: Percentage increase = (ΔA / A1) * 100.
Using a calculator or a programming language, we can substitute the values and calculate the final answer.
(34/32)^2 = 1.1289
so, a 12.89% increase
recall that area increases as the square of the linear scale factor