Question

One trampoline has a diameter of 10 feet. A larger trampoline has a diameter of 14 feet. How much greater is the area of the larger trampoline? Use 3.14 for π.

Answer 1

Answer:

The larger trampoline is larger in area by 75.36 feet²

Step-by-step explanation:

There are two trampolines here; the larger and the smaller one.

The trampoline's area can be found using the area of a circle which is πr² or πd²/4, where "r" and "d" represent radius and diameter respectively.

Here we will let D be the diameter of the larger trampoline and d should be taken as the diameter of the smaller trampoline.

So, the difference in area will be πD²/4 - πd²/4 = π/4 (D² - d²), where π is given as 3.14.

So, the area difference = $\frac{3.14}{4}$ × (14² - 10²) =  $\frac{3.14}{4}$ × (196 - 100) = $\frac{3.14}{4}$ × (96) = 75.36 feet²

Answer 2

Answer:

The second trampolline is 75.36 feet^2 greater than the first one.

Step-by-step explanation:

Assuming the trampolines are circullar their area will be given by:

A = \pi*(r^2)

The radius of a circle is r = d/2. So for the first trampoline we have:

A_1 = 3.14*[(10/2)^2] = 3.14*(25) = 78.5 feet^2

For the second trampoline we have:

A_2 = 3.14*[(14/2)^2] = 3.14*(49) = 153.86 feet^2

Difference between the areas:

A_2 - A_1 = 153.86 - 78.5 = 75.36 feet^2

From this we can say that the second trampolline is 75.36 feet^2 greater than the first one.