Question

The radius of the fruit is 3 times the radius of the seed. It is known that the seed has a volume of 100 cubic centimeters. What is the volume of edible fruit rounded to the nearest cubic centimeter?

Answer 1

The edible fruit=fruit-seed

alright

vsphere=4/3pir^3

so if the volume is 100
of the seed
$100=\frac{4}{3}\pi r^3$
find r
times both sides by 3/4
$75=\pi r^3$
divide both sides by pi
$\frac{75}{\pi}= r^3$
cube root both sides
$\sqrt[3]{\frac{75}{\pi}}= r$
this is the seed radius
3 times of taht is the radius of the fruit
$3\sqrt[3]{\frac{75}{\pi}}$=radiusfruit

input into equation
use radius fruit for r
$V=\frac{4}{3}\pi r^3$
$V=\frac{4}{3}\pi (3\sqrt[3]{\frac{75}{\pi}})^3$
$V=\frac{4}{3}\pi (27)(\frac{75}{\pi})$
$V=\frac{8100\pi}{3\pi}$
$V=2700 cm^3$

so the edible part is 2700-100=2600 cm³

Answer 2

Answer:

2600 cubic centimeters

Step-by-step explanation: