Question

Find the volume of the largest sphere that could be enclosed in a cube with a side length of 10 cm. Round to the nearest tenth.

Answer 1

Concept we will be using:
[tex]\text{i) Volume of a sphere}= \frac{4}{3} \pi r^3, \text{ where }r=\text{radius of the sphere}\\ \\ \text{ii) Diameter of the sphere = Side of the cube}\\[/tex]
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Solution:
Side of the cube = 10cm
Then, diameter of the sphere =side of the cube = 10cm

$\text{Radius of the sphere} = \frac{\text{Diameter}}{2} = \frac{10}{2}=5cm$

Plug in r=5 in the volume formula:

[tex]\text{i) Volume of the sphere}\\ \\ = \frac{4}{3} \pi r^3\\ \\ =\frac{4}{3} \pi (5)^3\\ \\ =\frac{4}{3} * \frac{22}{7} *125\\ \\ =523.809 cm^3 \\ \\ =523.8 cm^3[/tex]


Answer : 523.8 cubic cm.

Answer 2

Solution :-

Volume of the sphere = 4/3πr³

As the sphere is enclosed in the cube with side length 10 cm,
so, 
The diameter of the sphere = side length of the cube
Diameter of sphere = 10 cm 
Or, radius of the sphere = 10/2 = 5 cm

Volume of sphere = 4/3*22/7*5*5*5
= 11000/21
= 523.809 cm³
Or, 523.81 cm³ (Approx)

Answer.