Question

A solid sphere just fits inside a cube that has an edge length equal to the diameter of the sphere. The edge length of the cube is 5.8cm. What is the volume of air in the cube to the nearest cubic centimetre

Answer 1

Answer:

The volume of air in the cube is 93.004 cm³.

Step-by-step explanation:

Given : A solid sphere just fits inside a cube that has an edge length equal to the diameter of the sphere. The edge length of the cube is 5.8 cm.

To find : What is the volume of air in the cube to the nearest cubic centimeter?

Solution :

The edge length of the cube is 5.8 cm.

The volume of the cube is $V=a^3$

$V_c=(5.8)^3$

$V_c=195.112\ cm^3$

A solid sphere just fits inside a cube that has an edge length equal to the diameter of the sphere.

i.e. Diameter of sphere = 5.8 cm

The radius of sphere = $\frac{5.8}{2}=2.9\ cm$

The volume of the sphere is $V=\frac{4}{3}\pi r^3$

$V_s=\frac{4}{3}\times 3.14\times 2.9^3$

$V_s=102.108\ cm^3$

The volume of air in the cube = Volume of cube - Volume of sphere

The volume of air in the cube = 195.112 - 102.108

The volume of air in the cube is 93.004 cm³.