Question

Part II: Constructed Response15. An amusement park has two carousels. The first carousel has a circularplatform with a diameter of 13 meters, and the second carousel has acircular platform with a diameter of 19 meters. How much larger is thearea of the larger carousel's platform than the area of the smallercarousels platform? Show your work, using 3.14 for r.151st find Area of First Carousel:16. Next find Area of Second Carousel:127.6.417. What is the difference between the two areas?

Answer 1

- Area of First Carousel:

diameter = 13 m

$\text{Area}=\pi\cdot\frac{d^2}{4}=(3.14)\cdot\frac{(13)^2}{4}=3.14\cdot\frac{169}{4}=\frac{530.66}{4}=132.7m^2$

- Area of Second Carousel:

diameter = 19 m

$\text{Area}=(3.14)\cdot\frac{(19)^2}{4}=3.14\cdot\frac{361}{4}=\frac{1133.54}{4}=283.4m^2$

- The difference between the two areas is:

$283.4-132.7=150.7m^2$

Answer:

The platform area of the larger carousel is 150.7 m^2 larger than the platform area of the smaller carousel.