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?
27125\dfrac{27}{125}125
27​
(Choice B)
B
925\dfrac9{25}25
9​
(Choice C)
C
13\dfrac133
1​
(Choice D)
D
35\dfrac355
3​

Answer 1

Answer: $\frac{27}{125}$

Step-by-step explanation:

Since, the radius of the balloon 4 days ago = 5,

⇒  $\text{Volume of the balloon 4 days ago} =\frac{4}{3}\times \pi (5)^3$

$=\frac{4}{3}\pi(125)$

$=\frac{500}{3}\pi$

Now, if the radius is decreased by 0.5 cm each day,

Then the current radius of the balloon = 5 - 4 × 0.5 = 5 - 2 = 3 cm,

⇒  $\text{Volume of the balloon now} =\frac{4}{3}\times \pi (3)^3$

$=\frac{4}{3}\pi(27)$

$=\frac{108}{3}\pi$

Thus, the ratio of the current volume of the balloon to the volume of the balloon 4 days ago

$=\frac{\frac{108}{3}\pi}{\frac{500}{3}\pi}$

$=\frac{108}{500}$

$=\frac{27}{125}$

⇒ Option A is correct.