Question

Andy has a snowball (a perfect sphere) with the radius of 3 cm. He wanted the snowball to be bigger, so he spent four seconds packing more snow onto it. Each second he spent packing, the snowballs radius increases by 0.25 cm. What is the ratio of the current volume of the snow bar to the original volume of the snowball.

Answer 1

Answer:

Ratio = $\frac{64}{27}$

Step-by-step explanation:

Volume of Sphere is given by the formula:

$V=\frac{4}{3} \pi r^3$

Where

V is the volume

and

r is the radius

Original Volume, given r = 3, would be:

$V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (3)^3\\V=\frac{4}{3}\pi (27)\\V=36\pi$

Increased snowball volume:

Radius increased 0.25 per second, he spent 4 seconds, so radius increase:

0.25 * 4  = 1 cm

New radius = 3 + 1 = 4 cm

New Volume would be:

$V=\frac{4}{3} \pi r^3\\V=\frac{4}{3} \pi (4)^3\\V=\frac{4}{3}\pi(64)\\V=\frac{256\pi}{3}$

Ratio of New Volume to Original would be:

$Ratio=\frac{\frac{256\pi}{3}}{36\pi}=\frac{256\pi}{3}*\frac{1}{36\pi}=\frac{64}{27}$

This is the ratio for current volume to original volume.