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A particular spherical-shaped fruit has a spherical seed, and the rest of the fruit is edible.

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?

[tex]Volume=\frac{4}{3}\times \pi \times (3r)3\\\\Volume=\frac{4}{3}\times \pi \times 27r^3\\\\Volume=\frac{4}3}\times \pi r^3\times 27\\\\Volume=\text{Volume of seed}\times 27\\\\Volume=100\times 27\\\\Volume =2700\ cm^3[/tex]

Hence, the volume of edible fruit will be

2700-100=2600 cm³

Eduard22sly Eduard22sly · Answer 2 · 2022-04-25T18:14:50+02:00

The volume of the edible fruit rounded to the nearest cubic centimeter is 2600 cm³

How to determine the radius of the seed

Volume of seed (V) = 100 cm³
Pi (π) = 3.14
Radius of seed (r) =?

V = 4/3πr³

Cross multiply

4πr³ = 3V

Divide both side by 4π

r³ = 3V / 4π

Take the cube root

r = ³√(3V / 4π)

r = ³√[(3 × 100) / (4 × 3.14)]

r = 2.88 cm

How to determine the volume of the fruit

Radius of fruit (r) = 3 × radius of seed = 3 × 2.88 = 8.64 cm
Pi (π) = 3.14
Volume of fruit (V) =?

V = 4/3πr³

V = 4/3 × 3.14 × 8.64³

V = 2700 cm³

How to determine the volume of edible fruit

Volume of seed = 100 cm³
Volume of fruit = 2700 cm³
Volume of edible fruit =.?

Volume of edible fruit = Volume of fruit – Volume of seed

Volume of edible fruit = 2700 – 100

Volume of edible fruit = 2600 cm³

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