Question

4 days ago, Emily blew up a balloon (that is a perfect sphere) to a radius of 5 cm5\text{ cm}5 cm. Since then, the balloon has lost air and decreased by 0.5 cm0.5\text{ cm}0.5 cm each day.

What is the ratio of the current volume of the balloon to the volume of the balloon 444 days ago?

A) 27/25
B )9/25
C) 1/3
D) 3/5

PLEASE HELPP !!!!!!!!!!!!!

Answer 1

the correct answer is 27/125 (A)

Explanation:

i took the quiz

Answer 2

`\text{Ratio = }(27)/(125)`

Explanation:

Radius of the spherical balloon 4 days ago = 5 cm

`\text{Volume of sphere = }(4)/(3)\pi* radius^3\\\\\text{Volume of spherical balloon 4 days ago = }(4)/(3)\pi* 5^3`

Now, the radius of balloon decreases 0.5 cm each day

So, after 4 days the radius of balloon deceases by = 4 × 0.5

= 2 cm

So, current radius of spherical balloon = 5 -2 = 3 cm

`\text{Current Volume of spherical balloon = }(4)/(3)\pi* 3^3`

`\implies\text{Ratio of current volume to volume before 4 days = }((4)/(3)\pi* 3^3)/((4)/(3)\pi* 5^3)\\\\\implies Ratio = (3^3)/(5^3)\\\\\implies Ratio=(27)/(125)`